A096977 a(n) = 4*a(n-1) + 3*a(n-2) - 14*a(n-3) + 8*a(n-4).

0, 1, 2, 11, 36, 157, 598, 2447, 9672, 38913, 155194, 621683, 2484908, 9943269, 39765790, 159077719, 636281744, 2545185225, 10180624386, 40722730555, 162890456180, 651562756781, 2606249162982, 10425000380191, 41699994064216

Offset: 0

Author

Paul Barry, Jul 17 2004

Keywords

• easy
• nonn

Comments

Original name was: A Jacobsthal summation.

The convolution of A024000 and A003683. Inverse binomial transform is A055275, with interpolated zeros.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,3,-14,8).

Crossrefs

Cf. A001654.

Programs

Magma

[4*4^n/27-4*(-2)^n/27+n/9: n in [0..30]]; // Vincenzo Librandi, Jul 01 2011

Mathematica

LinearRecurrence[{4,3,-14,8},{0,1,2,11},30] (* Harvey P. Dale, Jul 01 2015 *)

PARI

a(n)=(4*4^n-4*(-2)^n+3*n)/27 \\ Charles R Greathouse IV, Jul 01 2011

Formula

G.f.: x*(1-2*x)/((1-x)^2*(1+2*x)*(1-4*x)).

a(n) = 4*4^n/27 - 4*(-2)^n/27 + n/9.

a(n) = Sum_{k=0..n} A001045(k)^2.

a(n) = 4*a(n-1) + 3*a(n-2) - 14*a(n-3) + 8*a(n-4).