# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a132469 Showing 1-1 of 1 %I A132469 #38 Mar 23 2023 17:17:23 %S A132469 0,1,33,1057,33825,1082401,34636833,1108378657,35468117025, %T A132469 1134979744801,36319351833633,1162219258676257,37191016277640225, %U A132469 1190112520884487201,38083600668303590433,1218675221385714893857,38997607084342876603425,1247923426698972051309601 %N A132469 a(n) = (2^(5*n) - 1)/31. %C A132469 Partial sums of powers of 32 (A009976), a.k.a. q-numbers for q=32. - _M. F. Hasler_, Nov 05 2012 %D A132469 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. %H A132469 Vincenzo Librandi, Table of n, a(n) for n = 0..600 %H A132469 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. %H A132469 Index entries related to partial sums. %H A132469 Index entries related to q-numbers. %H A132469 Index entries for linear recurrences with constant coefficients, signature (33,-32). %F A132469 a(n) = (32^n - 1)/31 = floor(32^n/31) = Sum_{k=0..n} 32^k. - _M. F. Hasler_, Nov 05 2012 %F A132469 G.f.: x/((1 - x)*(1 - 32*x)). - _Bruno Berselli_, Nov 06 2012 %F A132469 E.g.f.: exp(x)*(exp(31*x) - 1)/31. - _Stefano Spezia_, Mar 23 2023 %t A132469 Table[(2^(5 n) - 1)/31, {n, 16}] (* _Robert G. Wilson v_ *) %t A132469 LinearRecurrence[{33, -32}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 07 2012 *) %o A132469 (Sage) [gaussian_binomial(5*n,1,2)/31 for n in range(1,17)] # _Zerinvary Lajos_, May 28 2009 %o A132469 (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 %o A132469 (PARI) A132469(n)=32^n\31 \\ _M. F. Hasler_, Nov 07 2012 %o A132469 (Maxima) A132469(n):=(32^n-1)/31$ %o A132469 makelist(A132469(n),n,0,30); /* _Martin Ettl_, Nov 07 2012 */ %Y A132469 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. %K A132469 nonn,easy %O A132469 0,3 %A A132469 _A.K. Devaraj_, Aug 22 2007 %E A132469 Edited and extended by _Robert G. Wilson v_, Aug 22 2007 %E A132469 Edited and extended to offset 0 by _M. F. Hasler_, Nov 05 2012 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE