A008587 -id:A008587 - cp's OEIS frontend

A016885 a(n) = 5*n + 3.

3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 78, 83, 88, 93, 98, 103, 108, 113, 118, 123, 128, 133, 138, 143, 148, 153, 158, 163, 168, 173, 178, 183, 188, 193, 198, 203, 208, 213, 218, 223, 228, 233, 238, 243, 248, 253, 258, 263, 268, 273, 278, 283

Offset: 0

N. J. A. Sloane

Numbers ending in 3 or 8. - Lekraj Beedassy, Jul 08 2006

Number of moves in game of Brussels Sprouts with n+1 crosses. - Charles R Greathouse IV, Mar 09 2014

Elwyn R. Berlekamp, John Conway, and Richard K. Guy, Winning Ways for your Mathematical Plays, A K Peters, 2001.

G. C. Greubel, Table of n, a(n) for n = 0..5000
Teena Gerhardt and Brady Haran, Brussels Sprouts, Numberphile video (2014).
Lancelot Hogben, Choice and Chance by Cardpack and Chessboard, Vol. 1, Max Parrish and Co, London, 1950, p. 36.
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A001622, A008587, A016861, A016873.

Cf. similar sequences with closed form (2*k-1)*n+k listed in A269044.

List([0..60], n-> 5*n+3); # G. C. Greubel, Jul 05 2019

[5*n+3: n in [0..60]]; // G. C. Greubel, Jul 05 2019

Range[3, 300, 5] (* Vladimir Joseph Stephan Orlovsky, May 26 2011 *)

a(n)=5*n+3 \\ Charles R Greathouse IV, Mar 09 2014

a(n) = floor((15*n+10)/3). - Gary Detlefs, Mar 07 2010
G.f.: (3+2*x)/(1-x)^2. - Colin Barker, Jan 08 2012
E.g.f.: (3 + 5*x)*exp(x). - G. C. Greubel, Jul 05 2019
a(n) = 2*a(n-1)-a(n-2). - Wesley Ivan Hurt, Apr 22 2021
Sum_{n>=0} (-1)^n/a(n) = sqrt(2-2/sqrt(5))*Pi/10 - log(phi)/sqrt(5) + log(2)/5, where phi is the golden ratio (A001622). - Amiram Eldar, Apr 15 2023
a(n)^2 + (a(n)+1)^2 - n^2 = A017041(n)^2. - Charlie Marion, Apr 30 2023

More terms from James Sellers, Jul 06 2000

A047201 Numbers not divisible by 5.

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 29, 31, 32, 33, 34, 36, 37, 38, 39, 41, 42, 43, 44, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 58, 59, 61, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 74, 76, 77, 78, 79, 81, 82, 83, 84, 86, 87

Offset: 1

N. J. A. Sloane

Original name was: Numbers that are congruent to {1, 2, 3, 4} mod 5.
More generally the sequence of numbers not divisible by some fixed integer m>=2 is given by a(n,m) = n-1+floor((n+m-2)/(m-1)). - Benoit Cloitre, Jul 11 2009
Complement of A008587. - Reinhard Zumkeller, Nov 30 2009

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Cf. A019692, A045572, A179290.

a047201 n = a047201_list !! (n-1)
a047201_list = [x | x <- [1..], mod x 5 > 0]
-- Reinhard Zumkeller, Dec 17 2011

[Floor((15*n-1)/12): n in [1..70]]; // Vincenzo Librandi, Apr 06 2015

seq(floor((15*n-1)/12), n=1..56); # Gary Detlefs, Mar 07 2010

Select[Table[n,{n,200}],Mod[#,5]!=0&] (* Vladimir Joseph Stephan Orlovsky, Feb 18 2011 *)

a(n)= n+(n-1)\4 \\ corrected by Michel Marcus, Sep 02 2022

a(n)=n-1+floor((n+3)/4) \\ Benoit Cloitre, Jul 11 2009

def A047201(n): return n+(n-1>>2) # Chai Wah Wu, Feb 24 2025

[i for i in range(72) if gcd(5,i) == 1] # Zerinvary Lajos, Apr 21 2009

G.f.: (x+2*x^2+3*x^3+4*x^4+4*x^5+3*x^6+2*x^7+x^8)/(1-x^4)^2 (not reduced). - Len Smiley
a(n) = 5+a(n-4).
G.f.: x*(1+x+x^2+x^3+x^4)/((1-x)*(1-x^4)).
a(n) = n-1+floor((n+3)/4). - Benoit Cloitre, Jul 11 2009
A011558(a(n))=1; A079998(a(n))=0. - Reinhard Zumkeller, Nov 30 2009
a(n) = floor((15*n-1)/12). - Gary Detlefs, Mar 07 2010
a(n) = A225496(n) for n <= 42. - Reinhard Zumkeller, May 09 2013
From Wesley Ivan Hurt, Jun 22 2015: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5), n>5.
a(n) = (10*n-5-(-1)^n+2*(-1)^((2*n+5-(-1)^n)/4))/8. (End)
E.g.f.: 1 + (1/4)*(-cos(x) + (-3 + 5*x)*cosh(x) + sin(x) + (-2 + 5*x)*sinh(x)). - Stefano Spezia, Dec 01 2019
a(n) = floor((5*n-1)/4). - Wolfdieter Lang, Sep 30 2020
Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(2-2/sqrt(5))*Pi/5 = A179290 * A019692 / 10. - Amiram Eldar, Dec 07 2021

Comment from Lekraj Beedassy, Dec 17 2006 is now the current name. - Wesley Ivan Hurt, Jun 25 2015

A016897 a(n) = 5*n + 4.

Original entry on oeis.org

4, 9, 14, 19, 24, 29, 34, 39, 44, 49, 54, 59, 64, 69, 74, 79, 84, 89, 94, 99, 104, 109, 114, 119, 124, 129, 134, 139, 144, 149, 154, 159, 164, 169, 174, 179, 184, 189, 194, 199, 204, 209, 214, 219, 224, 229, 234, 239, 244, 249, 254, 259, 264, 269, 274, 279, 284

Offset: 0

N. J. A. Sloane

Except for 1, 2, n such that Sum_{k=1..n} (k mod 5)*C(n,k) is a power of 2. - Benoit Cloitre, Oct 17 2002
Numbers ending in 4 or 9. - Lekraj Beedassy, Jul 08 2006
The set of numbers congruent to 4 mod 5. - Gary Detlefs, Mar 07 2010
Also the number of (not necessarily maximal) cliques in the n-book graph and (n+1)-ladder graph. - Eric W. Weisstein, Nov 29 2017

Vincenzo Librandi, Table of n, a(n) for n = 0..2000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 944.
Tanya Khovanova, Recursive Sequences.
Leo Tavares, Illustration: Mirror Triangles.
Eric Weisstein's World of Mathematics, Book Graph.
Eric Weisstein's World of Mathematics, Clique.
Eric Weisstein's World of Mathematics, Ladder Graph.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A001622, A008587, A016861, A016873, A016885.

[5*n+4: n in [0..70]]; // Vincenzo Librandi, May 02 2011

a[1]:=4:for n from 2 to 100 do a[n]:=a[n-1]+5 od: seq(a[n], n=1..57); # Zerinvary Lajos, Mar 16 2008

Range[4, 500, 5] (* Vladimir Joseph Stephan Orlovsky, May 26 2011 *)
Table[5 n + 4, {n, 0, 20}] (* Eric W. Weisstein, Nov 29 2017 *)
5 Range[0, 20] + 4 (* Eric W. Weisstein, Nov 29 2017 *)
LinearRecurrence[{2, -1}, {9, 14}, {0, 20}] (* Eric W. Weisstein, Nov 29 2017 *)
CoefficientList[Series[(4 + x)/(-1 + x)^2, {x, 0, 20}], x] (* Eric W. Weisstein, Nov 29 2017 *)

a(n)=5*n+4 \\ Charles R Greathouse IV, Sep 24 2015

G.f.: (4+x)/(1-x)^2. - Paul Barry, Feb 27 2003
a(n) = 2*a(n-1) - a(n-2), n>1. - Philippe Deléham, Nov 03 2008
a(n) = A131098(n+2) + n + 1. - Jaroslav Krizek, Aug 15 2009
a(n) = 10*n - a(n-1) + 3, n>0. - Vincenzo Librandi, Nov 20 2010
A000041(a(n)) == 0 mod 5 is the first of Ramanujan's congruences. - Ivan N. Ianakiev, Dec 29 2014
a(n) = (n+2)^2 - 2*A000217(n-1). See Mirror Triangles illustration. - Leo Tavares, Aug 18 2021
Sum_{n>=0} (-1)^n/a(n) = sqrt(10*(5+sqrt(5)))*Pi/50 - log(2)/5 - sqrt(5)*log(phi)/5, where phi is the golden ratio (A001622). - Amiram Eldar, Dec 07 2021
E.g.f.: exp(x)*(4 + 5*x). - Elmo R. Oliveira, Mar 08 2024

A016873 a(n) = 5*n + 2.

Original entry on oeis.org

2, 7, 12, 17, 22, 27, 32, 37, 42, 47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97, 102, 107, 112, 117, 122, 127, 132, 137, 142, 147, 152, 157, 162, 167, 172, 177, 182, 187, 192, 197, 202, 207, 212, 217, 222, 227, 232, 237, 242, 247, 252, 257, 262, 267, 272, 277

Offset: 0

N. J. A. Sloane

Numbers ending in 2 or 7. - Lekraj Beedassy, Jul 08 2006
For n > 2, also the number of (not necessarily maximal) cliques in the n-gear graph. - Eric W. Weisstein, Nov 29 2017
Also, positive integers k such that 10*k+5 is equal to the product of two integers ending with 5. Proof: if 10*k+5 = (10*a+5) * (10*b+5), then k = 10*a*b + 5*(a+b) + 2 = 5 * (a + b + 2*a*b) + 2, of the form 5m + 2. So, 262 is a term because 2625 = 35 * 75. - Bernard Schott, May 15 2019
Numbers k such that 2^x + 3^x == 0 mod 31 and 2^x + 3^x == 0 mod 11 with x = 6*k+3. - Pedro Caceres, May 18 2022

G. C. Greubel, Table of n, a(n) for n = 0..1000
Cino Hilliard, solutions to 3^x + 5^x == 2 mod 11. [broken link]
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A001622, A008586, A008587, A016861, A342757.
Cf. A053742 (product of two integers ending with 5).
Cf. A324298 (product of two integers ending with 6).

[5*n+2: n in [0..80]]; // G. C. Greubel, Oct 17 2023

a[1]:=2:for n from 2 to 100 do a[n]:=a[n-1]+5 od: seq(a[n], n=1..50); # Zerinvary Lajos, Mar 16 2008

Range[2, 500, 5] (* Vladimir Joseph Stephan Orlovsky, May 26 2011 *)
(* Programs from Eric W. Weisstein, Nov 29 2017 *)
5*Range[0, 70] +2
LinearRecurrence[{2, -1}, {7, 12}, {0, 70}]
CoefficientList[Series[(2+3*x)/(1-x)^2, {x,0,70}], x] (* End *)

a(n)=5*n+2 \\ Charles R Greathouse IV, Jul 10 2016

[i+2 for i in range(300) if gcd(i,5) == 5] # Zerinvary Lajos, May 20 2009

a(n) = 10*n - a(n-1) - 1 (with a(0)=2). - Vincenzo Librandi, Nov 20 2010
G.f.: (2+3*x)/(1-x)^2. - Colin Barker, Jan 08 2012
E.g.f.: exp(x)*(2 + 5*x). - Stefano Spezia, Mar 21 2021
Sum_{n>=0} (-1)^n/a(n) = sqrt(2-2/sqrt(5))*Pi/10 + log(phi)/sqrt(5) - log(2)/5, where phi is the golden ratio (A001622). - Amiram Eldar, Apr 15 2023

A033429 a(n) = 5*n^2.

Original entry on oeis.org

0, 5, 20, 45, 80, 125, 180, 245, 320, 405, 500, 605, 720, 845, 980, 1125, 1280, 1445, 1620, 1805, 2000, 2205, 2420, 2645, 2880, 3125, 3380, 3645, 3920, 4205, 4500, 4805, 5120, 5445, 5780, 6125, 6480, 6845, 7220, 7605, 8000, 8405, 8820, 9245, 9680, 10125, 10580, 11045, 11520, 12005, 12500

Offset: 0

Jeff Burch

Number of edges of the complete bipartite graph of order 6n, K_n,5n. - Roberto E. Martinez II, Jan 07 2002
Number of edges of the complete tripartite graph of order 4n, K_n,n,2n. - Roberto E. Martinez II, Jan 07 2002
a(n+1)-a(n) : 5, 15, 25, 35, 45, ... (see A017329). - Philippe Deléham, Dec 08 2011
From Larry J Zimmermann, Feb 21 2013: (Start)
The sum of the areas of 2 squares that equals the area of a rectangle with whole number sides using the formula x^2 + y^2 = (x+y+sqrt(2*x*y))(x+y-sqrt(2*x*y)), where the substitution y=2*x obtains the whole number sides of the rectangle. So x^2+(2*x)^2=5x(x).
  x     squares sum      rectangle (l,w)   area
  1     1,4     5                   5,1    5
  2     4,16    20                  10,2   20  (End)

G. C. Greubel, Table of n, a(n) for n = 0..5000
Lancelot Hogben, Choice and Chance by Cardpack and Chessboard, Vol. 1, Max Parrish and Co, London, 1950, p. 36.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Central column of A055096.
Cf. A000290.
Cf. numbers of the form  n*(d*n+10-d)/2:  A008587, A056000, A028347, A140090, A014106, A028895, A045944, A186029, A007742, A022267, A022268, A049452, A186030, A135703, A152734, A139273.
Cf. A185019.
Cf. A001105, A033428.
Similar sequences are listed in A316466.

5*Range[50]^2 (* Alonso del Arte, May 23 2012 *)

PARI
```
a(n)=5*n^2
```

a(n) = 5*A000290(n). - Omar E. Pol, Dec 11 2008
From Bruno Berselli, Feb 11 2011: (Start)
G.f.: 5*x*(1+x)/(1-x)^3.
a(n) = 4*A000217(n) + A000567(n). (End)
a(n) = a(n-1)+5*(2*n-1) (with a(0)=0). - Vincenzo Librandi, Nov 17 2010
a(n) = A131242(10*n+4). - Philippe Deléham, Mar 27 2013
a(n) = a(n-1) + 10*n - 5, with a(0)=0. - Jean-Bernard François, Oct 04 2013
a(n) = A001105(n) + A033428(n). - Altug Alkan, Sep 28 2015
E.g.f.: 5*x*(x+1)*exp(x). - G. C. Greubel, Jul 17 2017
a(n) = Sum_{i = 2..6} P(i,n), where P(i,m) = m*((i-2)*m-(i-4))/2. - Bruno Berselli, Jul 04 2018
From Amiram Eldar, Feb 03 2021: (Start)
Sum_{n>=1} 1/a(n) = Pi^2/30.
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/60.
Product_{n>=1} (1 + 1/a(n)) = sqrt(5)*sinh(Pi/sqrt(5))/Pi.
Product_{n>=1} (1 - 1/a(n)) = sqrt(5)*sin(Pi/sqrt(5))/Pi. (End)

Better description from N. J. A. Sloane, May 15 1998

A121025 Multiples of 5 containing a 5 in their decimal representation.

Original entry on oeis.org

5, 15, 25, 35, 45, 50, 55, 65, 75, 85, 95, 105, 115, 125, 135, 145, 150, 155, 165, 175, 185, 195, 205, 215, 225, 235, 245, 250, 255, 265, 275, 285, 295, 305, 315, 325, 335, 345, 350, 355, 365, 375, 385, 395, 405, 415, 425, 435, 445, 450, 455, 465, 475, 485

Offset: 1

Reinhard Zumkeller, Jul 21 2006

Paolo Xausa, Table of n, a(n) for n = 1..10000 (terms 1..5000 from Muniru A Asiru)
Index entries for 10-automatic sequences.

Intersection of A008587 and A011535.

Cf. A121041, A011531, A121022, A121023, A121024, A121026, A121027, A121028, A121029, A121030, A121031, A121032, A121033, A121034, A121035, A121036, A121037, A121038, A121039, A121040.

Filtered([1..500],n-> n mod 5 = 0 and 5 in ListOfDigits(n)); # Muniru A Asiru, Feb 23 2019

Select[5*Range[200], MemberQ[IntegerDigits[#], 5] &] (* Paolo Xausa, Feb 25 2024 *)

is(n)=n%5==0 && setsearch(Set(digits(n)), 5) \\ Charles R Greathouse IV, Feb 12 2017

a(n) ~ 5n. - Charles R Greathouse IV, Feb 12 2017

Typo in comment fixed by Reinhard Zumkeller, May 01 2011

A140090 a(n) = n(3n + 7)/2.

Original entry on oeis.org

0, 5, 13, 24, 38, 55, 75, 98, 124, 153, 185, 220, 258, 299, 343, 390, 440, 493, 549, 608, 670, 735, 803, 874, 948, 1025, 1105, 1188, 1274, 1363, 1455, 1550, 1648, 1749, 1853, 1960, 2070, 2183, 2299, 2418, 2540, 2665, 2793, 2924

Offset: 0

Omar E. Pol, May 22 2008

This sequence is mentioned in the Guo-Niu Han's paper, chapter 6: Dictionary of the standard puzzle sequences, p. 19 (see link). - Omar E. Pol, Oct 28 2011

Number of cards needed to build an n-tier house of cards with a flat, one-card-wide roof. - Tyler Busby, Dec 28 2022

G. C. Greubel, Table of n, a(n) for n = 0..5000
Guo-Niu Han, Enumeration of Standard Puzzles, 2011. [Cached copy]
Guo-Niu Han, Enumeration of Standard Puzzles, arXiv:2006.14070 [math.CO], 2020.
Sela Fried, Counting r X s rectangles in nondecreasing and Smirnov words, arXiv:2406.18923 [math.CO], 2024. See p. 5.
Julie Zhang, Noah A. Rosenberg, and Julia A. Palacios, The space of multifurcating ranked tree shapes: enumeration, lattice structure, and Markov chains, arXiv:2506.10856 [math.PR], 2025. See p. 33.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

The generalized pentagonal numbers b*n+3*n*(n-1)/2, for b = 1 through 12, form sequences A000326, A005449, A045943, A115067, this sequence, A140091, A059845, A140672, A140673, A140674, A140675, A151542.

Cf. numbers of the form n*(d*n + 10 - d)/2: A008587, A056000, A028347, A014106, A028895, A045944, A186029, A007742, A022267, A033429, A022268, A049452, A186030, A135703, A152734, A139273.

LinearRecurrence[{3,-3,1},{0,5,13},50] (* Harvey P. Dale, Jan 17 2022 *)

a(n)=n*(3*n+7)/2 \\ Charles R Greathouse IV, Sep 24 2015

G.f.: x*(5 - 2*x)/(1 - x)^3. - Bruno Berselli, Feb 11 2011
a(n) = (3*n^2 + 7*n)/2.
a(n) = a(n-1) + 3*n + 2 (with a(0)=0). - Vincenzo Librandi, Nov 24 2010
E.g.f.: (1/2)*(3*x^2 + 10*x)*exp(x). - G. C. Greubel, Jul 17 2017
From Amiram Eldar, Feb 22 2022: (Start)
Sum_{n>=1} 1/a(n) = 117/98 - Pi/(7*sqrt(3)) - 3*log(3)/7.
Sum_{n>=1} (-1)^(n+1)/a(n) = 2*Pi/(7*sqrt(3)) + 4*log(2)/7 - 75/98. (End)

A008597 Multiples of 15.

Original entry on oeis.org

0, 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375, 390, 405, 420, 435, 450, 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, 735, 750, 765, 780

Offset: 0

N. J. A. Sloane

n such that the last decimal digit of F(n) is zero, where F(n) is the n-th Fibonacci number (F(45) = 1134903170). - Benoit Cloitre, Aug 07 2002

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Tanya Khovanova, Recursive Sequences.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 327.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A000045, A003893, A008585, A008587, A249674.

a008597 = (* 15)
a008597_list = [0, 15 ..]  -- Reinhard Zumkeller, Mar 09 2013

Range[0, 1005, 15] (* Vladimir Joseph Stephan Orlovsky, May 31 2011 *)
CoefficientList[Series[15 x / (x - 1)^2, {x, 0, 60}], x] (* Vincenzo Librandi, Jun 10 2013 *)

a(n)=15*n \\ Charles R Greathouse IV, Sep 24 2015

G.f.: 15*x/(1-x)^2. - Vincenzo Librandi, Jun 10 2013
From Elmo R. Oliveira, Apr 08 2025: (Start)
E.g.f.: 15*x*exp(x).
a(n) = A008585(A008587(n)) = A008587(A008585(n)) = A249674(n)/2. (End)

A079998 The characteristic function of the multiples of five.

Original entry on oeis.org

1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1

Offset: 0

Vladimir Baltic, Feb 10 2003

Number of permutations satisfying -k <= p(i) - i <= r and p(i) - i not in I, i = 1..n, with k = 2, r = 3, I = {-1, 0, 1, 2}.
a(n) = 1 if n = 5k, a(n) = 0 otherwise. Also, number of permutations satisfying -k <= p(i) - i <= r and p(i) - i not in I, i = 1..n, with k = 1, r = 4, I = {0, 1, 2, 3}.
a(n) is also the number of partitions of n with each part being five (a(0) = 1 because the empty partition has no parts to test equality with five). Hence a(n) is also the number of 2-regular graphs on n vertices with each component having girth exactly five. - Jason Kimberley, Oct 02 2011
This sequence is the Euler transformation of A185015. - Jason Kimberley, Oct 02 2011

D. H. Lehmer, Permutations with strongly restricted displacements. Combinatorial theory and its applications, II (Proc. Colloq., Balatonfured, 1969), pp. 755-770. North-Holland, Amsterdam, 1970.

Antti Karttunen, Table of n, a(n) for n = 0..16385
Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (April, 2010), 119-135.
Benoit Cloitre, A study of a family of self-referential sequences, arXiv:2506.18103 [math.GM], 2025. See p. 10.
Index entries for characteristic functions
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1).

Cf. A011558, A008587, A002524-A002529, A072827, A072850-A072856, A079955-A080014.

Characteristic function of multiples of g: A000007 (g = 0), A000012 (g = 1), A059841 (g = 2), A079978 (g = 3), A121262 (g = 4), this sequence (g = 5), A079979 (g = 6), A082784 (g = 7). - Jason Kimberley, Oct 14 2011

[Binomial(n-1,4) mod 5 : n in [0..100]]; // Wesley Ivan Hurt, Oct 06 2014

A079998:=n->binomial(n-1,4) mod 5: seq(A079998(n), n=0..100); # Wesley Ivan Hurt, Oct 06 2014

Table[Mod[Binomial[n - 1, 4], 5], {n, 0, 100}] (* Wesley Ivan Hurt, Oct 06 2014 *)
Table[Boole[Divisible[n, 5]], {n, 0, 99}] (* Alonso del Arte, Nov 29 2014 *)
PadRight[{},120,{1,0,0,0,0}] (* Harvey P. Dale, Jul 11 2023 *)

a(n)=!(n%5) \\ Charles R Greathouse IV, Mar 07 2012

(define (A079998 n) (if (zero? (modulo n 5)) 1 0)) ;; Antti Karttunen, Dec 21 2017

Recurrence: a(n) = a(n-5). G.f.: -1/(x^5 - 1).
a(n) = 1 - A011558(n); a(A008587(n)) = 1; a(A047201(n)) = 0. - Reinhard Zumkeller, Nov 30 2009
a(n) = floor(1/2*cos(2*n*Pi/5) + 1/2). - Gary Detlefs, May 16 2011
a(n) = floor(n/5) - floor((n-1)/5). - Tani Akinari, Oct 21 2012
a(n) = binomial(n - 1, 4) mod 5. - Wesley Ivan Hurt, Oct 06 2014

More terms from Antti Karttunen, Dec 21 2017

A008706 Coordination sequence for 3.3.3.4.4 planar net.

Original entry on oeis.org

1, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210, 215, 220, 225, 230, 235, 240, 245, 250, 255, 260, 265, 270, 275

Offset: 0

N. J. A. Sloane

Also the Engel expansion of exp^(1/5); cf. A006784 for the Engel expansion definition. - Benoit Cloitre, Mar 03 2002

			G.f. = 1 + 5*x + 10*x^2 + 15*x^3 + 20*x^4 + 25*x^5 + 30*x^6 + 35*x^7 + ...

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Brian Galebach, k-uniform tilings (k <= 6) and their A-numbers
Chaim Goodman-Strauss and N. J. A. Sloane, A Coloring Book Approach to Finding Coordination Sequences, Acta Cryst. A75 (2019), 121-134, also on NJAS's home page. Also arXiv:1803.08530.
Branko Grünbaum and Geoffrey C. Shephard, Tilings by regular polygons, Mathematics Magazine, 50 (1977), 227-247.
Tom Karzes, Tiling Coordination Sequences
Reticular Chemistry Structure Resource, cem
N. J. A. Sloane, The uniform planar nets and their A-numbers [Annotated scanned figure from Gruenbaum and Shephard (1977)]
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A006784, A048476 (binomial Transf.)
Essentially the same as A008587.
List of coordination sequences for uniform planar nets: A008458 (the planar net 3.3.3.3.3.3), A008486 (6^3), A008574 (4.4.4.4 and 3.4.6.4), A008576 (4.8.8), A008579 (3.6.3.6), A008706 (3.3.3.4.4), A072154 (4.6.12), A219529 (3.3.4.3.4), A250120 (3.3.3.3.6), A250122 (3.12.12).
First differences of A005891.

[0^n+5*n: n in [0..50] ]; // Vincenzo Librandi, Aug 21 2011

Join[{1}, LinearRecurrence[{2, -1}, {5, 10}, 100]] (* Jean-François Alcover, Dec 13 2018 *)

a(n)=0^n+5*n \\ Charles R Greathouse IV, Mar 19 2015

From Paul Barry, Jul 21 2003: (Start)
G.f.: (1 + 3*x + x^2)/(1 - x)^2.
a(n) = 0^n + 5n. (End)
G.f.: A(x) + 1, where A(x) is the g.f. of A008587. - Gennady Eremin, Feb 21 2021
E.g.f.: 1 + 5*x*exp(x). - Stefano Spezia, Jan 05 2023

cp's OEIS Frontend

A016885 a(n) = 5*n + 3.

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A047201 Numbers not divisible by 5.

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A016897 a(n) = 5*n + 4.

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A016873 a(n) = 5*n + 2.

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A033429 a(n) = 5*n^2.

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A121025 Multiples of 5 containing a 5 in their decimal representation.

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A140090 a(n) = n(3n + 7)/2.