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A099516 A transform of the Pell numbers. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 15 18:33 EDT 2021. Contains 345049 sequences. (Running on oeis4.)