OFFSET
0,8
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
V. E. Hoggatt, Jr., 7-page typed letter to N. J. A. Sloane with suggestions for new sequences, circa 1977.
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1,1).
FORMULA
From Colin Barker, Oct 17 2017: (Start)
G.f.: (1 - x)^5 / (1 - 6*x + 15*x^2 - 20*x^3 + 15*x^4 - 6*x^5 + x^6 - x^7).
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) + a(n-7) for n>6.
(End)
MAPLE
f:=n-> add( binomial(k, 6*(n-k)), k=0..n);
[seq(f(n), n=0..30)];
MATHEMATICA
Table[Sum[Binomial[k, 6(n-k)], {k, 0, n}], {n, 0, 40}] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1, 1}, {1, 1, 1, 1, 1, 1, 1}, 50] (* Harvey P. Dale, Apr 10 2022 *)
PROG
(PARI) Vec((1 - x)^5 / (1 - 6*x + 15*x^2 - 20*x^3 + 15*x^4 - 6*x^5 + x^6 - x^7) + O(x^30)) \\ Colin Barker, Oct 18 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Oct 17 2017
STATUS
approved