OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..474
Index entries for linear recurrences with constant coefficients, signature (71, 7585, -36991, -128).
FORMULA
Let b(n) = a(n) - 2^(7n)/7; then b(n) + 57*b(n-1) - 289*b(n-2) - b(n-3) = 0.
a(n) = 71*a(n-1) + 7585*a(n-2) - 36991*a(n-3) - 128*a(n-4); a(0)=1, a(1)=2, a(2)=3434, a(3)=232562. - Harvey P. Dale, May 06 2012
G.f.: (1 - 69*x - 4293*x^2 + 10569*x^3) / ((1 - 128*x)*(1 + 57*x - 289*x^2 - x^3)). - Colin Barker, May 27 2019
a(n) = (1 + 2*(s*(3 - 4*s^2))^(7*n) + 2*(-1)^n*((1 - 2*s^2)^(7*n) + s^(7*n))) * 2^(7*n)/7, where s = sin(Pi/14). - Vaclav Kotesovec, Apr 17 2023
MAPLE
A094211:=n->add(binomial(7*n, 7*k), k=0..n): seq(A094211(n), n=0..20); # Wesley Ivan Hurt, Feb 16 2017
MATHEMATICA
Table[Sum[Binomial[7n, 7k], {k, 0, n}], {n, 0, 20}] (* or *) LinearRecurrence[ {71, 7585, -36991, -128}, {1, 2, 3434, 232562}, 20] (* Harvey P. Dale, May 06 2012 *)
PROG
(PARI) a(n)=sum(k=0, n, binomial(7*n, 7*k))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Benoit Cloitre, May 27 2004
STATUS
approved