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A132469 a(n) = (2^(5n)-1)/31. 32
0, 1, 33, 1057, 33825, 1082401, 34636833, 1108378657, 35468117025, 1134979744801, 36319351833633, 1162219258676257, 37191016277640225, 1190112520884487201, 38083600668303590433, 1218675221385714893857, 38997607084342876603425 (list; graph; refs; listen; history; text; internal format)
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 related to partial sums.

Index entries related to q-numbers.

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]

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 xrange(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

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.

Sequence in context: A170666 A170714 A170752 * A200441 A206939 A188604

Adjacent sequences:  A132466 A132467 A132468 * A132470 A132471 A132472

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

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Last modified February 18 23:26 EST 2018. Contains 299330 sequences. (Running on oeis4.)