OFFSET
0,2
REFERENCES
Matthijs Coster, Supercongruences, Thesis, Jun 08, 1988.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..554
Index entries for linear recurrences with constant coefficients, signature (38,1691,-1728).
FORMULA
G.f.: (1-36x-841x^2+288x^3)/((1-x)(1+27x)(1-64x)). a(n) = ((-27)^n + 1)/3 + (64^n +0^n)/6.
Let b(n)=a(n)-2^(6n)/6 then b(n)+26*b(n-1)-27*b(n-2)=0 - Benoit Cloitre, May 27 2004
MATHEMATICA
Table[Sum[Binomial[6n, 6k], {k, 0, n}], {n, 0, 20}] (* or *) LinearRecurrence[ {38, 1691, -1728}, {1, 2, 926, 37130}, 30] (* Harvey P. Dale, Jun 19 2021 *)
PROG
(PARI) a(n)=sum(k=0, n, binomial(6*n, 6*k))
(PARI) a(n)=if(n<0, 0, (2*(-27)^n+2+64^n+0^n)/6)
(PARI) a(n)=if(n<0, 0, polsym(x*(x-64)*(x+27)^2*(x-1)^2, n)[n+1]/6)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Sebastian Gutierrez and Sarah Kolitz (skolitz(AT)mit.edu), May 16 2002
STATUS
approved