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A101893 a(n) = sum_{k=0..floor(n/2)} C(n,2k)*Pell(k). 2
0, 0, 1, 3, 8, 20, 50, 126, 320, 816, 2084, 5324, 13600, 34736, 88712, 226552, 578560, 1477504, 3773200, 9635888, 24607872, 62842944, 160486688, 409846752, 1046656000, 2672922880, 6826040896, 17432165568, 44517810688, 113688426240 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Transform of Pell numbers under the mapping g(x)-> (1/(1-x))g(x^2/((1-x)^2).

Binomial transform of aerated Pell numbers 0,0,1,0,2,0,5,0,12,...

LINKS

Andrew Woods, Table of n, a(n) for n = 0..100

Index entries for linear recurrences with constant coefficients, signature (4,-4,0,2).

FORMULA

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

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

a(n) = sum_{k=0..n} binomial(n, k) * A000129(k/2) * (1+(-1)^k)/2.

MATHEMATICA

CoefficientList[Series[x^2*(1-x)/(1 - 4*x + 4*x^2 - 2*x^4), {x, 0, 40}], x] (* Vaclav Kotesovec, Jan 05 2015 *)

LinearRecurrence[{4, -4, 0, 2}, {0, 0, 1, 3}, 30] (* Harvey P. Dale, Aug 05 2018 *)

CROSSREFS

Cf. A000129 (Pell numbers), A135248 (partial sums).

Sequence in context: A122595 A026582 A187003 * A140662 A174198 A077997

Adjacent sequences:  A101890 A101891 A101892 * A101894 A101895 A101896

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Dec 22 2004

STATUS

approved

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Last modified September 23 09:03 EDT 2020. Contains 337298 sequences. (Running on oeis4.)