A016933 -id:A016933 - cp's OEIS frontend

A017293 a(n) = 10*n + 2.

2, 12, 22, 32, 42, 52, 62, 72, 82, 92, 102, 112, 122, 132, 142, 152, 162, 172, 182, 192, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 302, 312, 322, 332, 342, 352, 362, 372, 382, 392, 402, 412, 422, 432, 442, 452, 462, 472, 482, 492, 502, 512, 522, 532

Offset: 0

N. J. A. Sloane, Dec 11 1996

Number of 5 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (11;0) and (01;1). An occurrence of a ranpp (xy;z) in a matrix A=(a(i,j)) is a triple (a(i1,j1), a(i1,j2), a(i2,j1)) where i1A008574; m=3: A016933; m=4: A022144; m=6: A017569. - Sergey Kitaev, Nov 13 2004

Vincenzo Librandi, Table of n, a(n) for n = 0..5000
Tanya Khovanova, Recursive Sequences.
Sergey Kitaev, On multi-avoidance of right angled numbered polyomino patterns, Integers: Electronic Journal of Combinatorial Number Theory 4 (2004), A21, 20pp.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Subsequence of A034709, together with A017281, A139222, A139245, A017329, A139249, A139264, A139279 and A139280.

Cf. A008574, A008592, A016861, A016873, A016933, A017569, A022144.

[10*n+2: n in [0..50]]; // Vincenzo Librandi, May 04 2011

A017293:=n->10*n+2; seq(A017293(n), n=0..100); # Wesley Ivan Hurt, May 03 2014

Range[2, 1000, 10] (* Vladimir Joseph Stephan Orlovsky, May 28 2011 *)
CoefficientList[Series[(2 + 8 x) / (1 - x)^2, {x, 0, 30}], x] (* Vincenzo Librandi, Jul 23 2016 *)
10 Range[0,60]+2 (* or *) LinearRecurrence[{2,-1},{2,12},60] (* Harvey P. Dale, Jul 04 2019 *)

a(n) = 2*A016861(n) = A008592(n) + 2. - Wesley Ivan Hurt, May 03 2014
G.f.: 2*(1 + 4*x)/(1-x)^2. - Vincenzo Librandi, Jul 23 2016
From Elmo R. Oliveira, Apr 04 2025: (Start)
E.g.f.: 2*exp(x)*(1 + 5*x).
a(n) = 2*a(n-1) - a(n-2) for n >= 2.
a(n) = A016873(2*n). (End)

A089911 a(n) = Fibonacci(n) mod 12.

Original entry on oeis.org

0, 1, 1, 2, 3, 5, 8, 1, 9, 10, 7, 5, 0, 5, 5, 10, 3, 1, 4, 5, 9, 2, 11, 1, 0, 1, 1, 2, 3, 5, 8, 1, 9, 10, 7, 5, 0, 5, 5, 10, 3, 1, 4, 5, 9, 2, 11, 1, 0, 1, 1, 2, 3, 5, 8, 1, 9, 10, 7, 5, 0, 5, 5, 10, 3, 1, 4, 5, 9, 2, 11, 1, 0, 1, 1, 2, 3, 5, 8, 1, 9, 10, 7, 5, 0, 5, 5, 10, 3, 1, 4, 5, 9, 2, 11, 1, 0, 1, 1

Offset: 0

Casey Mongoven, Nov 14 2003

From Reinhard Zumkeller, Jul 05 2013: (Start)
Sequence has been applied by several composers to 12-tone equal temperament pitch structure. The complete Fibonacci mod 12 system (a set of 10 periodic sequences) exhausts all possible ordered dyads; that is, every possible combination of two pitches is found in these sets.
a(A008594(n)) = 0;
a(A227144(n)) = 1;
a(3*A047522(n)) = 2;
a(A017569(n)) = a(2*A016933(n)) = a(4*A016777(n)) = 3;
a(2*A017629(n)) = a(3*A017137(n)) = a(6*A004767(n)) = 4;
a(A227146(n)) = 5;
a(nonexistent) = 6;
a(2*A017581(n)) = 7;
a(2*A017557(n)) = a(4*A016813(n)) = 8;
a(A017617(n)) = a(2*A016957(n)) = a(4*A016789(n)) = 9;
a(3*A047621(n)) = 10;
a(2*A017653(n)) = 11. (End)

Reinhard Zumkeller, Table of n, a(n) for n = 0..1199
Ron Knott, Fibonacci Numbers and the Golden Section
M. Renault, The Fibonacci Sequence Modulo M
A. P. Shah, Fibonacci Sequence Modulo m, Fibonacci Quarterly, Vol.6, No.2 (1968), 139-141.
D. D. Wall, Fibonacci series modulo m, Amer. Math. Monthly, 67 (1960), 525-532.
Index entries for linear recurrences with constant coefficients, signature (1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1).

Cf. A000045, A001175, A003893, A010881.

a089911 n = a089911_list !! n
a089911_list = 0 : 1 : zipWith (\u v -> (u + v) `mod` 12)
                       (tail a089911_list) a089911_list
-- Reinhard Zumkeller, Jul 01 2013

[Fibonacci(n) mod 12: n in [0..100]]; // Vincenzo Librandi, Feb 04 2014

with(combinat,fibonacci); A089911 := proc(n) fibonacci(n) mod 12; end;

Table[Mod[Fibonacci[n], 12], {n, 0, 100}] (* Vincenzo Librandi, Feb 04 2014 *)

a(n)=fibonacci(n)%12 \\ Charles R Greathouse IV, Feb 03 2014

Has period of 24, restricted period 12 and multiplier 5.

a(n) = (a(n-1) + a(n-2)) mod 12, a(0) = 0, a(1) = 1.

More terms from Ray Chandler, Nov 15 2003

A013730 a(n) = 2^(3*n+1).

Original entry on oeis.org

2, 16, 128, 1024, 8192, 65536, 524288, 4194304, 33554432, 268435456, 2147483648, 17179869184, 137438953472, 1099511627776, 8796093022208, 70368744177664, 562949953421312, 4503599627370496, 36028797018963968, 288230376151711744, 2305843009213693952, 18446744073709551616

Offset: 0

N. J. A. Sloane

1/2 + 1/16 + 1/128 + 1/1024 + ... = 4/7. - Gary W. Adamson, Aug 29 2008

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (8).
Index to divisibility sequences.

Cf. A013731, A016921, A016933, A132024, A157176.

[2^(3*n+1): n in [0..30]]; // Vincenzo Librandi, May 04 2011

seq(2^(3*n+1),n=0..19); # Nathaniel Johnston, Jun 26 2011

Table[2^n, {n, 1, 100, 3}] (* Vladimir Joseph Stephan Orlovsky, Jun 14 2011 *)
2^(3 Range[0, 40] + 1) (* Vladimir Joseph Stephan Orlovsky, Jun 14 2011 *)
Table[2^(3 n + 1), {n, 0, 20}] (* Eric W. Weisstein, Nov 03 2024 *)
2^(3 Range[0, 20] + 1) (* Eric W. Weisstein, Nov 03 2024 *)
2^Range[1, 61, 3] (* Eric W. Weisstein, Nov 03 2024 *)
LinearRecurrence[{8}, {2}, 20] (* Eric W. Weisstein, Nov 03 2024 *)
CoefficientList[Series[2/(1 - 8 x), {x, 0, 20}], x] (* Eric W. Weisstein, Nov 03 2024 *)

a(n)=2<<(3*n) \\ Charles R Greathouse IV, Jun 14 2011

From Philippe Deléham, Nov 23 2008: (Start)
a(n) = 8*a(n-1), n > 0; a(0)=2.
G.f.: 2/(1-8x). (End)
a(n) = A157176(A016921(n)) = A157176(A016933(n)). - Reinhard Zumkeller, Feb 24 2009
From Amiram Eldar, May 08 2023: (Start)
Sum_{n>=0} (-1)^n/a(n) = 4/9.
Product_{n>=0} (1 - 1/a(n)) = A132024. (End)
E.g.f.: 2*exp(8*x). - Stefano Spezia, May 29 2024

A017569 a(n) = 12*n + 4.

Original entry on oeis.org

4, 16, 28, 40, 52, 64, 76, 88, 100, 112, 124, 136, 148, 160, 172, 184, 196, 208, 220, 232, 244, 256, 268, 280, 292, 304, 316, 328, 340, 352, 364, 376, 388, 400, 412, 424, 436, 448, 460, 472, 484, 496, 508, 520, 532, 544, 556, 568, 580, 592, 604, 616, 628

Offset: 0

N. J. A. Sloane

Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0(46).
Number of 6 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (11;0) and (01;1). An occurrence of a ranpp (xy;z) in a matrix A=(a(i,j)) is a triple (a(i1,j1), a(i1,j2), a(i2,j1)) where i1A008574; m=3: A016933; m=4: A022144; m=5: A017293. - Sergey Kitaev, Nov 13 2004
Except for 4, exponents e such that x^e - x^2 + 1 is reducible.
If Y and Z are 2-blocks of a (3n+1)-set X then a(n-1) is the number of 3-subsets of X intersecting both Y and Z. - Milan Janjic, Oct 28 2007
Terms are perfect squares iff n is a generalized octagonal number (A001082), then n = k*(3*k-2) and a(n) = (2*(3*k-1))^2. - Bernard Schott, Feb 26 2023

Vincenzo Librandi, Table of n, a(n) for n = 0..5000
Milan Janjic, Two Enumerative Functions.
Tanya Khovanova, Recursive Sequences.
Sergey Kitaev, On multi-avoidance of right angled numbered polyomino patterns, Integers: Electronic Journal of Combinatorial Number Theory, Vol. 4 (2004), Article A21, 20pp.
William A. Stein, Dimensions of the spaces S_k(Gamma_0(N)).
William A. Stein, The modular forms database.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A008594, A017533, A017545, A089911.
Cf. A016777, A016933, A017293, A022144.
Cf. A001082.

a017569 = (+ 4) . (* 12)  -- Reinhard Zumkeller, Jul 05 2013

[12*n+4: n in [0..50]]; // Vincenzo Librandi, May 04 2011

12*Range[0,200]+4 (* Vladimir Joseph Stephan Orlovsky, Feb 19 2011 *)

A089911(a(n)) = 3. - Reinhard Zumkeller, Jul 05 2013
Sum_{n>=0} (-1)^n/a(n) = sqrt(3)*Pi/36 + log(2)/12. - Amiram Eldar, Dec 12 2021
From Stefano Spezia, Feb 25 2023: (Start)
O.g.f.: 4*(1 + 2*x)/(1 - x)^2.
E.g.f.: 4*exp(x)*(1 + 3*x). (End)
From Elmo R. Oliveira, Apr 10 2025: (Start)
a(n) = 2*a(n-1) - a(n-2).
a(n) = 2*A016933(n) = 4*A016777(n) = A016777(4*n+1). (End)

A016935 a(n) = (6*n + 2)^3.

Original entry on oeis.org

8, 512, 2744, 8000, 17576, 32768, 54872, 85184, 125000, 175616, 238328, 314432, 405224, 512000, 636056, 778688, 941192, 1124864, 1331000, 1560896, 1815848, 2097152, 2406104, 2744000, 3112136

Offset: 0

N. J. A. Sloane

The generating function is 8 times the g.f. of A016779. - R. J. Mathar, May 07 2008

			a(1) = (6*1 + 2)^3 = 8^3 = 512.

Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Cf. A002117, A016779, A016911, A016923, A016933, A016959, A016971.

[(6*n+2)^3: n in [0..50]]; // Vincenzo Librandi, May 04 2011

(6*Range[0,30]+2)^3 (* or *) LinearRecurrence[{4,-6,4,-1},{8,512,2744,8000},30] (* Harvey P. Dale, Aug 23 2019 *)

a(n) = 8*A016779(n). - R. J. Mathar, May 07 2008
Sum_{n>=0} 1/a(n) = Pi^3 / (324*sqrt(3)) + 13*zeta(3)/216. - Amiram Eldar, Oct 02 2020
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Wesley Ivan Hurt, Oct 02 2020
G.f.: 8*(1+60*x+93*x^2+8*x^3)/(-1+x)^4. - Wesley Ivan Hurt, Oct 02 2020

A017617 a(n) = 12*n + 8.

Original entry on oeis.org

8, 20, 32, 44, 56, 68, 80, 92, 104, 116, 128, 140, 152, 164, 176, 188, 200, 212, 224, 236, 248, 260, 272, 284, 296, 308, 320, 332, 344, 356, 368, 380, 392, 404, 416, 428, 440, 452, 464, 476, 488, 500, 512, 524, 536, 548, 560, 572, 584, 596, 608, 620, 632, 644, 656

Offset: 0

N. J. A. Sloane

Also the number of cube units that frame a cube of edge length n+1. - Peter M. Chema, Mar 27 2016

			For n=3; a(3)= 12*3 + 8 = 44.
Thus, there are 44 cube units that frame a cube of edge length 4. - _Peter M. Chema_, Mar 26 2016

Vincenzo Librandi, Table of n, a(n) for n = 0..3000
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A008594, A016789, A016933, A016957, A017533, A017545, A089911.

a017617 = (+ 8) . (* 12)  -- Reinhard Zumkeller, Jul 05 2013

[12*n+8: n in [0..60]]; // Vincenzo Librandi, Jun 08 2011

12*Range[0,200]+8 (* Vladimir Joseph Stephan Orlovsky, Feb 19 2011 *)

my(x='x+O('x^99)); Vec(4*(2+x)/(1-x)^2) \\ Altug Alkan, Mar 27 2016

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jun 08 2011
A089911(a(n)) = 9. - Reinhard Zumkeller, Jul 05 2013
G.f.: 12*x/(1-x)^2 + 8/(1-x) = 4*(2+x)/(1-x)^2. (see the PARI program). - Wolfdieter Lang, Oct 11 2021
Sum_{n>=0} (-1)^n/a(n) = sqrt(3)*Pi/36 - log(2)/12. - Amiram Eldar, Dec 12 2021
From Elmo R. Oliveira, Apr 04 2025: (Start)
E.g.f.: 4*exp(x)*(2 + 3*x).
a(n) = 4*A016789(n) = 2*A016957(n) = A016933(2*n+1). (End)

A339013 Class number m containing n in a partitioning of the natural numbers into classes B_m by William J. Keith.

Original entry on oeis.org

2, 3, 2, 4, 2, 4, 2, 3, 2, 5, 2, 5, 2, 3, 2, 5, 2, 5, 2, 3, 2, 5, 2, 5, 2, 3, 2, 4, 2, 4, 2, 3, 2, 6, 2, 6, 2, 3, 2, 6, 2, 6, 2, 3, 2, 6, 2, 6, 2, 3, 2, 4, 2, 4, 2, 3, 2, 6, 2, 6, 2, 3, 2, 6, 2, 6, 2, 3, 2, 6, 2, 6, 2, 3, 2, 4, 2, 4, 2, 3, 2, 6, 2, 6, 2, 3, 2

Offset: 1

Kevin Ryde, Nov 19 2020

a(n)=m when n is in class B_m. Keith's residues formula in lemma 1 is equivalent to requiring that n-1 in factorial base representation ends in m-2 nonzero digits, so m = A339012(n-1) + 2.
a(n)=m iff n mod m! is among certain residue classes determined by m. The residues for A339012 are rows of A227157 and here add +1 to each residue (mod m!).  For example 3 or 5 (mod 24) in A339012 becomes here 4 or 6 (mod 24).
The frequency of appearance of the term k = 2, 3, ... in this sequence is 1/(k*(k-1)). - Amiram Eldar, Feb 15 2021

Kevin Ryde, Table of n, a(n) for n = 1..10080
William J. Keith, Sequences of Density zeta(K) - 1, INTEGERS, Vol. 10 (2010), Article #A19, pp. 233-241. Also arXiv preprint, arXiv:0905.3765 [math.NT], 2009 and author's copy.

Cf. A005408 (class B_2), A016933 (class B_3).

Cf. A161189 (class number in partition A_k), A339012.

a[n_] := Module[{k = n - 1, m = 2, r}, While[{k, r} = QuotientRemainder[k, m]; r != 0, m++]; m]; Array[a, 30] (* Amiram Eldar, Feb 15 2021 after Kevin Ryde's PARI code *)

a(n) = n--; my(b=2,r); while([n,r]=divrem(n,b);r!=0, b++); b;

a(n) = A339012(n-1) + 2.
a(n) = m iff n == 1 + Sum_{j=1..m-2} d[j]*j! (mod m!) with d[j] in ranges 1 <= d[j] <= j. [Keith, section 2.1 lemma 1]
a(n)=2 iff n mod 2 = 1. [Keith section 4 residues].
a(n)=3 iff n mod 6 = 2.
a(n)=4 iff n mod 24 = 4 or 6.
a(n)=5 iff n mod 120 = any of 10, 12, 16, 18, 22, 24.

A144390 a(n) = 3*n^2 - n - 1.

Original entry on oeis.org

1, 9, 23, 43, 69, 101, 139, 183, 233, 289, 351, 419, 493, 573, 659, 751, 849, 953, 1063, 1179, 1301, 1429, 1563, 1703, 1849, 2001, 2159, 2323, 2493, 2669, 2851, 3039, 3233, 3433, 3639, 3851, 4069, 4293, 4523, 4759, 5001, 5249, 5503, 5763, 6029, 6301, 6579

Offset: 1

Paul Curtz, Oct 02 2008

Sequence's original Name was "First bisection of A135370."

The partial sums of this sequence give A081437. - Leo Tavares, Dec 26 2021

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
John Elias, Illustration: Belted Hexagrams
Leo Tavares, Illustration: Bounded Hexagons
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A016933, A049450, A144391.
Cf. A003215, A005408, A016754, A002378.
Cf. A081437 (partial sums).

[3*n^2-n-1: n in [1..60]]; // Vincenzo Librandi, Jun 14 2011

A144390:=n->3*n^2-n-1; seq(A144390(n), n=1..50); # Wesley Ivan Hurt, Mar 26 2014

Table[3*n^2 -n -1 , {n,0,50}] (* G. C. Greubel, Jul 19 2017 *)

a(n)=3*n^2-n-1 \\ Charles R Greathouse IV, Oct 07 2015

a(n+1) = a(n) + 6*n + 2; see A016933.
G.f.: x*(1+6*x-x^2)/(1-x)^3. a(n) = A049450(n)-1. - R. J. Mathar, Oct 24 2008
a(-n) = A144391(n). - Michael Somos, Mar 27 2014
E.g.f.: (3*x^2 + 2*x -1)*exp(x) + 1. - G. C. Greubel, Jul 19 2017
From Leo Tavares, Dec 26 2021: (Start)
a(n) = A003215(n) - 2*A005408(n). See Bounded Hexagons illustration.
a(n) = A016754(n-1) - A002378(n-2). (End)
a(n) = A003154(n) - A049451(n-1). - John Elias, Dec 22 2022

Edited by R. J. Mathar, Oct 24 2008

More terms from Vladimir Joseph Stephan Orlovsky, Oct 25 2008

A016934 a(n) = (6*n + 2)^2.

Original entry on oeis.org

4, 64, 196, 400, 676, 1024, 1444, 1936, 2500, 3136, 3844, 4624, 5476, 6400, 7396, 8464, 9604, 10816, 12100, 13456, 14884, 16384, 17956, 19600, 21316, 23104, 24964, 26896, 28900, 30976, 33124, 35344, 37636, 40000, 42436, 44944, 47524, 50176, 52900, 55696, 58564

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A016922, A016933, A086728.

[(6*n+2)^2: n in [0..50]]; // Vincenzo Librandi, May 04 2011

(6*Range[0,40]+2)^2 (* or *) LinearRecurrence[{3,-3,1},{4,64,196},40] (* Harvey P. Dale, Nov 22 2013 *)

a(n)=(6*n+2)^2 \\ Charles R Greathouse IV, Jun 17 2017

Sum_{n>=0} 1/a(n) = A086728. - Amiram Eldar, Nov 16 2020
From Stefano Spezia, Feb 21 2025: (Start)
G.f.: 4*(1 + 13*x + 4*x^2)/(1 - x)^3.
E.g.f.: 4*exp(x)*(1 + 15*x + 9*x^2). (End)

A221683 T(n,k)=Number of 0..k arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0.

Original entry on oeis.org

0, 0, 2, 0, 2, 4, 0, 2, 5, 8, 0, 2, 5, 14, 16, 0, 2, 5, 20, 40, 32, 0, 2, 5, 26, 68, 113, 64, 0, 2, 5, 32, 100, 241, 320, 128, 0, 2, 5, 38, 133, 418, 844, 906, 256, 0, 2, 5, 44, 166, 636, 1692, 2966, 2565, 512, 0, 2, 5, 50, 199, 891, 2856, 6932, 10413, 7262, 1024, 0, 2, 5, 56, 232

Offset: 1

R. H. Hardin Jan 22 2013

Table starts
....0.....0......0.......0.......0........0........0........0........0
....2.....2......2.......2.......2........2........2........2........2
....4.....5......5.......5.......5........5........5........5........5
....8....14.....20......26......32.......38.......44.......50.......56
...16....40.....68.....100.....133......166......199......232......265
...32...113....241.....418.....636......891.....1182.....1509.....1872
...64...320....844....1692....2856.....4326.....6102.....8184....10572
..128...906...2966....6932...13169....21985....33710....48674....67202
..256..2565..10413...28288...60120...109567...180382...276317...401105
..512..7262..36568..115604..275632...551027...980490..1606710..2476200
.1024.20560.128408..472188.1261451..2759757..5289023..9228224.15012528
.2048.58209.450913.1929012.5777107.13846871.28634131.53334307.91896348

			Some solutions for n=6 k=4
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....0....1....1....1....1....0....0....0....0....1....0....0....0....0....1
..2....0....0....0....4....1....4....4....0....2....1....1....1....0....0....2
..1....2....3....1....3....2....3....3....1....3....3....1....2....0....1....3
..1....1....4....2....2....1....2....3....4....2....3....1....1....0....1....0
..0....2....4....2....1....0....3....4....4....2....4....2....1....1....2....1

R. H. Hardin, Table of n, a(n) for n = 1..2080

Row 4 is A016933

Empirical for column k:
k=1: a(n) = 2*a(n-1) for n>2
k=2: a(n) = 2*a(n-1) +2*a(n-2) +a(n-3)
k=3: a(n) = 3*a(n-1) +2*a(n-2) -a(n-3) +a(n-4)
k=4: a(n) = 3*a(n-1) +4*a(n-2) +6*a(n-4) +4*a(n-5) +4*a(n-6)
k=5: a(n) = 4*a(n-1) +3*a(n-2) -6*a(n-3) +19*a(n-4) +5*a(n-5) +a(n-6)
k=6: a(n) = 4*a(n-1) +5*a(n-2) -7*a(n-3) +33*a(n-4) +17*a(n-5) +24*a(n-6) -5*a(n-7) +2*a(n-8)
k=7: a(n) = 5*a(n-1) +3*a(n-2) -16*a(n-3) +65*a(n-4) -14*a(n-5) +23*a(n-6) +2*a(n-7) +8*a(n-8)
Empirical for row n:
n=1: a(n) = 0
n=2: a(n) = 2
n=3: a(n) = 5 for n>1
n=4: a(n) = 6*n + 2
n=5: a(n) = 33*n - 32 for n>3
n=6: a(n) = 18*n^2 + 57*n - 99 for n>4
n=7: a(n) = 153*n^2 - 213*n + 96 for n>3

cp's OEIS Frontend

A017293 a(n) = 10*n + 2.

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A089911 a(n) = Fibonacci(n) mod 12.

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A013730 a(n) = 2^(3*n+1).

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Magma

Maple

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A017569 a(n) = 12*n + 4.

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Magma

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A016935 a(n) = (6*n + 2)^3.

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Magma

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A017617 a(n) = 12*n + 8.

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A339013 Class number m containing n in a partitioning of the natural numbers into classes B_m by William J. Keith.