OFFSET
2,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (11,-31,21).
FORMULA
a(n) = (1/3!)*(11-6*3^n+7^n).
a(n) = 11*a(n-1)-31*a(n-2)+21*a(n-3). G.f.: -x^2*(21*x+1) / ((x-1)*(3*x-1)*(7*x-1)). - Colin Barker, Jul 12 2013
a(n) = sum(i=0..n, (-1)^i * C(n,i) * C(2^(n-i)-1,3) ). - Geoffrey Critzer, Aug 24 2014
MAPLE
seq((11-6*3^n+7^n)/6, n=2..50); # Robert Israel, Aug 25 2014
MATHEMATICA
nn = 19; Table[Sum[(-1)^i Binomial[n, i] Binomial[2^(n - i) - 1, 3], {i, 0, n}], {n, 2, nn}] (* Geoffrey Critzer, Aug 24 2014 *)
Table[(11 - 6*3^n + 7^n)/6, {n, 2, 20}] (* Wesley Ivan Hurt, Aug 26 2014 *)
PROG
(Magma) [(11-6*3^n+7^n)/6 : n in [2..30]]; // Wesley Ivan Hurt, Aug 26 2014
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, May 31 2004
EXTENSIONS
More terms from Colin Barker, Jul 12 2013
STATUS
approved