A213785 a(n) = Sum(P(i)*P(j), 1<=i<j<=n), where P(k) is the k-th Pell number A000129(k).

0, 0, 2, 17, 113, 693, 4123, 24234, 141738, 827298, 4824716, 28127435, 163955435, 955642695, 5569991317, 32464523892, 189217679988, 1102842830628, 6427842380918, 37464218883749, 218357488856453, 1272680757553593, 7417727160997231, 43233682460792670

Offset

0,3

Comments

Suggested by A190173.

Links

Bruno Berselli, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (9,-20,8,5,-1).

Formula

G.f.: x^2*(2-x)/((1-x)*(1-6*x+x^2)*(1-2*x-x^2)). [Bruno Berselli, Jun 20 2012]

a(n) = 9*a(n-1) -20*a(n-2) +8*a(n-3) +5*a(n-4) -a(n-5). - Vincenzo Librandi, Jun 20 2012

Mathematica

LinearRecurrence[{9, -20, 8, 5, -1}, {0, 0, 2, 17, 113}, 30] (* Vincenzo Librandi, Jun 20 2012 *)

Prog

(Magma) I:=[0, 0, 2, 17, 113]; [n le 5 select I[n] else 9*Self(n-1)-20*Self(n-2)+8*Self(n-3)+5*Self(n-4)-Self(n-5): n in [1..30]]; // Vincenzo Librandi, Jun 20 2012

Crossrefs

Cf. A000129, A213788, A190173.

Sequence in context: A155845 A115354 A100274 * A198158 A203247 A294271

Adjacent sequences: A213782 A213783 A213784 * A213786 A213787 A213788

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 20 2012

Status

approved