A132469 a(n) = (2^(5*n) - 1)/31.

0, 1, 33, 1057, 33825, 1082401, 34636833, 1108378657, 35468117025, 1134979744801, 36319351833633, 1162219258676257, 37191016277640225, 1190112520884487201, 38083600668303590433, 1218675221385714893857, 38997607084342876603425, 1247923426698972051309601

Offset: 0

Author

A.K. Devaraj, Aug 22 2007

Keywords

• nonn
• easy

Comments

Partial sums of powers of 32 (A009976), a.k.a. q-numbers for q=32. - M. F. Hasler, Nov 05 2012

References

• A. K. Devaraj, "Minimum Universal Exponent Generalisation of Fermat's Theorem", in ISSN #1550-3747, Proceedings of Hawaii Intl Conference on Statistics, Mathematics & Related Fields, 2004.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..600
• Quynh Nguyen, Jean Pedersen, and Hien T. Vu, New Integer Sequences Arising From 3-Period Folding Numbers, Vol. 19 (2016), Article 16.3.1. See Table 1.
• Index entries related to partial sums.
• Index entries related to q-numbers.
• Index entries for linear recurrences with constant coefficients, signature (33,-32).

Crossrefs

Cf. similar sequences of the form (k^n-1)/(k-1): A000225, A003462, A002450, A003463, A003464, A023000, A023001, A002452, A002275, A016123, A016125, A091030, A135519, A135518, A131865, A091045, A218721, A218722, A064108, A218724-A218734, A132469, A218736-A218753, A133853, A094028, A218723.

Programs

Magma

[n le 2 select n-1 else 33*Self(n-1) - 32*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012

Mathematica

Table[(2^(5 n) - 1)/31, {n, 16}] (* Robert G. Wilson v *)
LinearRecurrence[{33, -32}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)

Maxima

A132469(n):=(32^n-1)/31$
makelist(A132469(n),n,0,30); /* Martin Ettl, Nov 07 2012 */

PARI

A132469(n)=32^n\31  \\ M. F. Hasler, Nov 07 2012

Sage

[gaussian_binomial(5*n,1,2)/31 for n in range(1,17)] # Zerinvary Lajos, May 28 2009

Formula

a(n) = (32^n - 1)/31 = floor(32^n/31) = Sum_{k=0..n} 32^k. - M. F. Hasler, Nov 05 2012

G.f.: x/((1 - x)*(1 - 32*x)). - Bruno Berselli, Nov 06 2012

E.g.f.: exp(x)*(exp(31*x) - 1)/31. - Stefano Spezia, Mar 23 2023

Extensions

Edited and extended by Robert G. Wilson v, Aug 22 2007

Edited and extended to offset 0 by M. F. Hasler, Nov 05 2012