cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A015196 Sum of Gaussian binomial coefficients for q=10.

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%I A015196 #20 May 14 2019 09:38:28
%S A015196 1,2,13,224,13435,2266646,1348019857,2269339773068,13484735901526279,
%T A015196 226960944509263279490,13485189809930561625032701,
%U A015196 2269636415245291711513986785912,1348523520252401463276762566348539123
%N A015196 Sum of Gaussian binomial coefficients for q=10.
%D A015196 J. Goldman and G.-C. Rota, The number of subspaces of a vector space, pp. 75-83 of W. T. Tutte, editor, Recent Progress in Combinatorics. Academic Press, NY, 1969.
%D A015196 I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
%D A015196 M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
%H A015196 Vincenzo Librandi, <a href="/A015196/b015196.txt">Table of n, a(n) for n = 0..60</a>
%H A015196 Kent E. Morrison, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL9/Morrison/morrison37.html">Integer Sequences and Matrices Over Finite Fields</a>, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.
%F A015196 a(n) = 2*a(n-1)+(10^(n-1)-1)*a(n-2), (Goldman + Rota, 1969). - _Vaclav Kotesovec_, Aug 21 2013
%F A015196 a(n) ~ c * 10^(n^2/4), where c = EllipticTheta[3,0,1/10]/QPochhammer[1/10,1/10] = 1.348524024616... if n is even and c = EllipticTheta[2,0,1/10]/QPochhammer[1/10,1/10] = 1.2763120346269... if n is odd. - _Vaclav Kotesovec_, Aug 21 2013
%t A015196 Total/@Table[QBinomial[n, m, 10], {n, 0, 20}, {m, 0, n}] (* _Vincenzo Librandi_, Nov 01 2012 *)
%t A015196 Flatten[{1,RecurrenceTable[{a[n]==2*a[n-1]+(10^(n-1)-1)*a[n-2],a[0]==1,a[1]==2},a,{n,1,15}]}] (* _Vaclav Kotesovec_, Aug 21 2013 *)
%Y A015196 Cf. A006116, A006117, A006118, A006119, A006120, A006121, A006122, A015195.
%Y A015196 Row sums of triangle A022174.
%K A015196 nonn
%O A015196 0,2
%A A015196 _N. J. A. Sloane_, _Olivier Gérard_