login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A006120 Sum of Gaussian binomial coefficients [ n,k ] for q=6.
(Formerly M1952)
5
1, 2, 9, 88, 2111, 118182, 16649389, 5547079988, 4671840869691, 9326302435784002, 47100039978152210249, 564020035264998031552848, 17088883834526416216141122391, 1227783027118593811726444427584862, 223195138386683651821176756496371359589 (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
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)+(6^(n-1)-1)*a(n-2), (Goldman + Rota, 1969). - Vaclav Kotesovec, Aug 21 2013
a(n) ~ c * 6^(n^2/4), where c = EllipticTheta[3,0,1/6]/QPochhammer[1/6,1/6] = 1.656816524577... if n is even and c = EllipticTheta[2,0,1/6]/QPochhammer[1/6,1/6] = 1.630173070572... if n is odd. - Vaclav Kotesovec, Aug 21 2013
MATHEMATICA
Flatten[{1, RecurrenceTable[{a[n]==2*a[n-1]+(6^(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, 6], {k, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Aug 13 2016 *)
PROG
(Magma) [n le 2 select n else 2*Self(n-1)+(6^(n-2)-1)*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Aug 13 2016
CROSSREFS
Sequence in context: A228509 A361607 A001192 * A012941 A216691 A059477
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 25 07:53 EDT 2024. Contains 371964 sequences. (Running on oeis4.)