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

0,3

Comments

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

Links

Table of n, a(n) for n=0..30.

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

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)}.

Mathematica

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

Crossrefs

Cf. A099505, A099508.

Sequence in context: A317535 A087640 A116953 * A293741 A291559 A297074

Adjacent sequences: A099513 A099514 A099515 * A099517 A099518 A099519

Keyword

easy,nonn

Author

Paul Barry, Oct 20 2004

Status

approved