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A015196 Sum of Gaussian binomial coefficients for q=10. 3
1, 2, 13, 224, 13435, 2266646, 1348019857, 2269339773068, 13484735901526279, 226960944509263279490, 13485189809930561625032701, 2269636415245291711513986785912, 1348523520252401463276762566348539123 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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.

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.

M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..60

Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.

FORMULA

a(n) = 2*a(n-1)+(10^(n-1)-1)*a(n-2), (Goldman + Rota, 1969). - Vaclav Kotesovec, Aug 21 2013

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

MATHEMATICA

Total/@Table[QBinomial[n, m, 10], {n, 0, 20}, {m, 0, n}] (* Vincenzo Librandi, Nov 01 2012 *)

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 *)

CROSSREFS

Cf. A006116, A006117, A006118, A006119, A006120, A006121, A006122, A015195.

Row sums of triangle A022174.

Sequence in context: A259795 A069569 A255882 * A236903 A277452 A268703

Adjacent sequences:  A015193 A015194 A015195 * A015197 A015198 A015199

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Olivier Gérard

STATUS

approved

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Last modified May 12 04:27 EDT 2021. Contains 343810 sequences. (Running on oeis4.)