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A006121 Sum of Gaussian binomial coefficients [ n,k ] for q=7.
(Formerly M1984)
5
1, 2, 10, 116, 3652, 285704, 61946920, 33736398032, 51083363186704, 194585754101247008, 2061787082699360148640, 54969782721182164414355264 (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.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..65

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

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

FORMULA

a(n) = 2*a(n-1)+(7^(n-1)-1)*a(n-2), (Goldman + Rota, 1969). - Vaclav Kotesovec, Aug 21 2013

a(n) ~ c * 7^(n^2/4), where c = EllipticTheta[3,0,1/7]/QPochhammer[1/7,1/7] = 1.537469386940... if n is even and c = EllipticTheta[2,0,1/7]/QPochhammer[1/7,1/7] = 1.499386995418... if n is odd. - Vaclav Kotesovec, Aug 21 2013

MATHEMATICA

Flatten[{1, RecurrenceTable[{a[n]==2*a[n-1]+(7^(n-1)-1)*a[n-2], a[0]==1, a[1]==2}, a, {n, 1, 15}]}] (* Vaclav Kotesovec, Aug 21 2013 *)

Table[Sum[QBinomial[n, k, 7], {k, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Aug 13 2016 *)

PROG

(MAGMA) [n le 2 select n else 2*Self(n-1)+(7^(n-2)-1)*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Aug 13 2016

CROSSREFS

Sequence in context: A187653 A131811 A261496 * A110951 A172477 A265942

Adjacent sequences:  A006118 A006119 A006120 * A006122 A006123 A006124

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified March 20 23:22 EDT 2019. Contains 321354 sequences. (Running on oeis4.)