A217777 - OEIS

A217777

Expansion of (1+x)*(1+2*x)*(1-x)/(1-5*x^2+5*x^4).

1, 2, 4, 8, 15, 30, 55, 110, 200, 400, 725, 1450, 2625, 5250, 9500, 19000, 34375, 68750, 124375, 248750, 450000, 900000, 1628125, 3256250, 5890625, 11781250, 21312500, 42625000, 77109375, 154218750, 278984375, 557968750, 1009375000, 2018750000, 3651953125

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OFFSET

0,2

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0, 5, 0, -5).

FORMULA

a(n) = A216212(n+1)/2.

a(2n) = A039717(n+1), a(2n+1) = 2*a(2n) = 2*A039717(n+1).

a(n) = sum(A217770(n-k,k), 0<=k<=n).

a(n) = 5*a(n-2) - 5*a(n-4) for n>=4, a(0) = 1, a(1) = 2, a(2) = 4, a(3) = 8.

G.f.: (1+x)*(1+2*x)*(1-x)/(1-5*x^2+5*x^4).

MATHEMATICA

CoefficientList[Series[(1+x)(1+2x)(1-x)/(1-5x^2+5x^4), {x, 0, 50}], x] (* or *) LinearRecurrence[{0, 5, 0, -5}, {1, 2, 4, 8}, 50] (* Harvey P. Dale, Jan 11 2026 *)

PROG

(PARI) Vec((1+x)*(1+2*x)*(1-x)/(1-5*x^2+5*x^4)+O(x^66)) /* Joerg Arndt, Mar 29 2013 */

CROSSREFS

Cf. A217770

Sequence in context: A293335 A344687 A301480 * A034338 A166861 A026023

Adjacent sequences: A217774 A217775 A217776 * A217778 A217779 A217780

KEYWORD

nonn,easy

AUTHOR

Philippe Deléham, Mar 24 2013

EXTENSIONS

Corrected name (g.f.), Joerg Arndt, Mar 29 2013

STATUS

approved