A099516 A transform of the Pell numbers.

0, 1, 2, 5, 10, 23, 50, 112, 246, 545, 1202, 2658, 5870, 12972, 28656, 63315, 139880, 309049, 682790, 1508527, 3332850, 7363430, 16268356, 35942447, 79409300, 175442668, 387613604, 856372740, 1892023992, 4180136405, 9235369230

Offset: 0

Author

Paul Barry, Oct 20 2004

Keywords

• easy
• nonn

Comments

A transform of A000129 under the mapping g(x)->(1/(1+x^3))g(x/(1+x^3))

Links

• Index entries for linear recurrences with constant coefficients, signature (2,1,-2,2,0,-1).

Crossrefs

Cf. A099505, A099508.

Programs

Mathematica

LinearRecurrence[{2,1,-2,2,0,-1},{0,1,2,5,10,23},40] (* Harvey P. Dale, Apr 15 2015 *)

Formula

G.f.: x/(1-2x-x^2+2x^3-2x^4+x^6); a(n)=2a(n-1)+a(n-2)-2a(n-3)+2a(n-4)-a(n-6); a(n)=sum{k=0..floor(n/3), binomial(n-2k, k)(-1)^k*Pell(n-3k)}.