A016897 -id:A016897 - cp's OEIS frontend

A001545 a(n) = (5n+1)(5*n+4).

4, 54, 154, 304, 504, 754, 1054, 1404, 1804, 2254, 2754, 3304, 3904, 4554, 5254, 6004, 6804, 7654, 8554, 9504, 10504, 11554, 12654, 13804, 15004, 16254, 17554, 18904, 20304, 21754, 23254, 24804, 26404, 28054, 29754, 31504, 33304, 35154, 37054, 39004, 41004, 43054

Offset: 0

N. J. A. Sloane

T. D. Noe, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A000217, A001622, A016861, A016897, A177059, A200135, A200138.

Table[(5n+1)(5n+4),{n,0,60}] (* or *) LinearRecurrence[{3,-3,1},{4,54,154},60] (* Harvey P. Dale, Mar 17 2019 *)

a(n)=(5*n+1)*(5*n+4) \\ Charles R Greathouse IV, Jun 17 2017

a(n) = 50*A000217(n) + 4.
a(n) = 50*n + a(n-1) with a(0)=4. - Vincenzo Librandi, Jan 20 2011
From Amiram Eldar, Jan 23 2022: (Start)
Sum_{n>=0} 1/a(n) = sqrt(1 + 2/sqrt(5))*Pi/15 = 0.2882687....
Sum_{n>=0} (-1)^n/a(n) = 2*log(phi)/(3*sqrt(5)) + 2*log(2)/15, where phi is the golden ratio (A001622).
Product_{n>=0} (1 - 1/a(n)) = sqrt(2 + 2/sqrt(5)) * cos(sqrt(13)*Pi/10).
Product_{n>=0} (1 + 1/a(n)) = sqrt(2 + 2/sqrt(5)) * cos(Pi/(2*sqrt(5))).
Product_{n>=0} (1 + 2/a(n)) = phi. (End)
G.f.: 2*(2+21*x+2*x^2)/(1-x)^3. - R. J. Mathar, May 30 2022
Sum_{n>=0} 1/a(n) = (Psi(4/5) - Psi(1/5))/15. See A200135, A200138. - R. J. Mathar, May 30 2022
From Elmo R. Oliveira, Oct 23 2024: (Start)
E.g.f.: exp(x)*(4 + 25*x*(2 + x)).
a(n) = A016861(n)*A016897(n).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

A013829 a(n) = 3^(5*n + 4).

Original entry on oeis.org

81, 19683, 4782969, 1162261467, 282429536481, 68630377364883, 16677181699666569, 4052555153018976267, 984770902183611232881, 239299329230617529590083, 58149737003040059690390169, 14130386091738734504764811067

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (243).

Cf. A000244, A016897.

[3^(5*n+4): n in [0..15]]; // Vincenzo Librandi, Jul 07 2011

NestList[243#&,81,12] (* Harvey P. Dale, Jan 23 2016 *)

makelist(3^(5*n+4),n,0,20); /* Martin Ettl, Oct 21 2012 */

a(n)=3^(5*n+4) \\ Charles R Greathouse IV, Jul 11 2016

From Philippe Deléham, Nov 26 2008: (Start)
a(n) = 243*a(n-1); a(0)=81.
G.f.: 81/(1-243*x). (End)
a(n) = A000244(A016897(n)). - Wesley Ivan Hurt, Sep 04 2022

A013857 a(n) = 10^(5*n + 4).

Original entry on oeis.org

10000, 1000000000, 100000000000000, 10000000000000000000, 1000000000000000000000000, 100000000000000000000000000000, 10000000000000000000000000000000000, 1000000000000000000000000000000000000000, 100000000000000000000000000000000000000000000

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..50
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (100000).

Subsequence of A011557.

Cf. A016897.

[10^(5*n+4): n in [0..10]]; // Vincenzo Librandi, Jul 08 2011

10^(5 Range[0,10]+4) (* or *) LinearRecurrence[{100000},{10000},20] (* Harvey P. Dale, Mar 15 2023 *)

From Elmo R. Oliveira, Mar 02 2025: (Start)
G.f.: 10000/(1 - 100000*x).
E.g.f.: 10000*exp(100000*x).
a(n) = A011557(A016897(n)). (End)

A013833 a(n) = 4^(5*n + 4).

Original entry on oeis.org

256, 262144, 268435456, 274877906944, 281474976710656, 288230376151711744, 295147905179352825856, 302231454903657293676544, 309485009821345068724781056, 316912650057057350374175801344, 324518553658426726783156020576256

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..100
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (1024).

Cf. A000302 (4^n), A016897 (5*n+4).

[4^(5*n+4): n in [0..15]]; // Vincenzo Librandi, Jul 07 2011

4^(5*Range[0, 10] + 4) (* Paul F. Marrero Romero, Sep 30 2024 *)
NestList[1024#&,256,20] (* Harvey P. Dale, Jun 06 2025 *)

From Philippe Deléham, Nov 30 2008: (Start)
a(n) = 1024*a(n-1), n > 0; a(0)=256.
G.f.: 256/(1-1024*x).
a(n) = 4*A013832(n). (End)

A013837 a(n) = 5^(5*n + 4).

Original entry on oeis.org

625, 1953125, 6103515625, 19073486328125, 59604644775390625, 186264514923095703125, 582076609134674072265625, 1818989403545856475830078125, 5684341886080801486968994140625, 17763568394002504646778106689453125

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..100
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (3125).

Cf. A000351 (5^n), A016897 (5*n+4).

[5^(5*n+4): n in [0..15]]; // Vincenzo Librandi, Jul 07 2011

From Philippe Deléham, Dec 03 2008: (Start)
a(n) = 3125*a(n-1), n > 0; a(0)=625.
G.f.: 625/(1-3125*x). (End)

A013861 a(n) = 11^(5*n+4).

Original entry on oeis.org

14641, 2357947691, 379749833583241, 61159090448414546291, 9849732675807611094711841, 1586309297171491574414436704891, 255476698618765889551019445759400441, 41144777789250865278081232758997200423491

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..100
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (161051).

Cf. A001020 (11^n), A016897 (5*n+4).

[11^(5*n+4): n in [0..10]]; // Vincenzo Librandi, Jul 08 2011

A013861:=n->11^(5*n+4): seq(A013861(n), n=0..10); # Wesley Ivan Hurt, May 02 2017

11^(5Range[0,10]+4) (* Harvey P. Dale, Mar 21 2011 *)

A013881 16^(5*n+4).

Original entry on oeis.org

65536, 68719476736, 72057594037927936, 75557863725914323419136, 79228162514264337593543950336, 83076749736557242056487941267521536, 87112285931760246646623899502532662132736, 91343852333181432387730302044767688728495783936

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..100
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (1048576).

[16^(5*n+4): n in [0..10]]; // Vincenzo Librandi, Jul 10 2011

16^(5*Range[0,10]+4) (* or *) NestList[1048576#&,65536,10] (* Harvey P. Dale, Jul 21 2024 *)

A013881(n):=16^(5*n+4)$
makelist(A013881(n),n,0,10); /* Martin Ettl, Nov 12 2012 */

Vec(65536/(1-1048576*x) + O(x^20)) \\ Colin Barker, Feb 28 2015

a(n) = 1048576*a(n-1). - Colin Barker, Feb 28 2015
G.f.: 65536 / (1-1048576*x). - Colin Barker, Feb 28 2015
a(n) = A001025(A016897(n)). - Michel Marcus, Feb 28 2015

A013897 a(n) = 20^(5*n + 4).

Original entry on oeis.org

160000, 512000000000, 1638400000000000000, 5242880000000000000000000, 16777216000000000000000000000000, 53687091200000000000000000000000000000, 171798691840000000000000000000000000000000000, 549755813888000000000000000000000000000000000000000

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..50
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (3200000).

Subsequence of A009964.

Cf. A013825, A013857, A016897.

[20^(5*n+4): n in [0..10]]; // Vincenzo Librandi, May 27 2011

20^(5*Range[0,10]+4) (* or *) NestList[3200000#&,160000,10] (* Harvey P. Dale, Feb 15 2016 *)

a(n) = 3200000*a(n-1), a(0)=160000. - Vincenzo Librandi, May 27 2011
From Elmo R. Oliveira, Jul 11 2025: (Start)
G.f.: 160000/(1-3200000*x).
E.g.f.: 160000*exp(3200000*x).
a(n) = A013825(n)*A013857(n) = A009964(A016897(n)). (End)

A013905 22^(5n+4).

Original entry on oeis.org

234256, 1207269217792, 6221821273427820544, 32064977213018365645815808, 165251092644282265779977014214656, 851643319086537701956194499721106030592, 4389056261830591470007906571986683114651910144, 22619580800770514778759787562400873673529752979243008

Offset: 0

N. J. A. Sloane, Dec 11 1996

Vincenzo Librandi, Table of n, a(n) for n = 0..50
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (5153632).

[22^(5*n+4): n in [0..10]]; // Vincenzo Librandi, May 28 2011

A013905:=n->22^(5*n+4); seq(A013905(n), n=0..10); # Wesley Ivan Hurt, May 08 2014

Table[22^(5 n + 4), {n, 0, 10}] (* Wesley Ivan Hurt, May 08 2014 *)

a(n) = 5153632*a(n-1), a(0)=234256. - Vincenzo Librandi, May 28 2011

a(n) = 22^A016897(n) = A010810(5n+4) = A010810(A016897(n)). - Wesley Ivan Hurt, May 08 2014

A016900 a(n) = (5*n + 4)^4.

Original entry on oeis.org

256, 6561, 38416, 130321, 331776, 707281, 1336336, 2313441, 3748096, 5764801, 8503056, 12117361, 16777216, 22667121, 29986576, 38950081, 49787136, 62742241, 78074896, 96059601, 116985856, 141158161

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

Cf. A000583, A016897.

[(5*n+4)^4: n in [0..50]]; // Vincenzo Librandi, May 02 2011

A016900:=n->(5*n + 4)^4; seq(A016900(n), n=0..50); # Wesley Ivan Hurt, Feb 15 2014

Table[(5 n + 4)^4, {n, 0, 50}] (* Wesley Ivan Hurt, Feb 15 2014 *)

a(n)=(5*n+4)^4 \\ Charles R Greathouse IV, Feb 18 2014

From R. J. Mathar, Mar 01 2010: (Start)
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
G.f.: (256 + 5281*x + 8171*x^2 + 1291*x^3 + x^4)/(1 - x)^5. (End)
a(n) = A016897(n)^4 = A000583(A016897(n)). - Wesley Ivan Hurt, Feb 15 2014

cp's OEIS Frontend

A001545 a(n) = (5*n+1)*(5*n+4).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A013829 a(n) = 3^(5*n + 4).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

Maxima

PARI

Formula

A013857 a(n) = 10^(5*n + 4).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

Formula

A013833 a(n) = 4^(5*n + 4).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

Formula

A013837 a(n) = 5^(5*n + 4).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Formula

A013861 a(n) = 11^(5*n+4).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Maple

Mathematica

A013881 16^(5*n+4).

Views

Author

Keywords

Links

Programs

Magma

Mathematica

Maxima

PARI

Formula

A013897 a(n) = 20^(5*n + 4).

Views

Author

Keywords

Links

Crossrefs

Programs

A001545 a(n) = (5n+1)(5*n+4).