OFFSET
0,3
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 for linear recurrences with constant coefficients, signature (33,-32).
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
MATHEMATICA
Table[(2^(5 n) - 1)/31, {n, 16}] (* Robert G. Wilson v *)
LinearRecurrence[{33, -32}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)
PROG
(Sage) [gaussian_binomial(5*n, 1, 2)/31 for n in range(1, 17)] # Zerinvary Lajos, May 28 2009
(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
(PARI) A132469(n)=32^n\31 \\ M. F. Hasler, Nov 07 2012
(Maxima) A132469(n):=(32^n-1)/31$
makelist(A132469(n), n, 0, 30); /* Martin Ettl, Nov 07 2012 */
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
A.K. Devaraj, Aug 22 2007
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
STATUS
approved