OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..500
D. Birmajer, J. B. Gil, and M. D. Weiner, On the Enumeration of Restricted Words over a Finite Alphabet, J. Int. Seq. 19 (2016) # 16.1.3, example 16.
Index entries for linear recurrences with constant coefficients, signature (8,-21,35,-35,21,-7,1).
FORMULA
G.f.: 1/((1-x)^7 - x);
Equals A099239(n, 7).
a(n) = 8*a(n-1) -21*a(n-2) +35*a(n-3) -35*a(n-4) +21*a(n-5) -7*a(n-6) +a(n-7).
a(n) = Sum_{k=0..n} binomial(7*n - 6*(k-1), k).
a(n) = Sum_{k=0..n} binomial(n + 6*(k+1), k + 6*(k+1)).
a(n) = Sum_{k=0..n} binomial(n + 6*(k+1), n-k).
MATHEMATICA
Table[Sum[Binomial[7*n-6*(j-1), j], {j, 0, n}], {n, 0, 30}] (* G. C. Greubel, Mar 09 2021 *)
PROG
(Sage) [sum(binomial(7*n-6*j+6, j) for j in (0..n)) for n in (0..30)] # G. C. Greubel, Mar 09 2021
(Magma) [(&+[Binomial(7*n-6*j+6, j): j in [0..n]]): n in [0..30]]; // G. C. Greubel, Mar 09 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 08 2004
STATUS
approved