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A097112
Expansion of (1+4x-6x^2-36x^3)/(1-19x^2+90x^4).
0
1, 4, 13, 40, 157, 400, 1813, 4000, 20317, 40000, 222853, 400000, 2405677, 4000000, 25651093, 40000000, 270859837, 400000000, 2837738533, 4000000000, 29539646797, 40000000000, 305856821173, 400000000000, 3152711390557
OFFSET
0,2
FORMULA
G.f. : 4(1+x)/(1-10x^2)-3/(1-9x^2); a(n)=19a(n-2)-90a(n-4); a(n)=(2+sqrt(10)/5)(sqrt(10))^n+(2-sqrt(10)/5)(-sqrt(10))^n-3^(n+1)(1+(-1)^n)/2; a(n)=sum{k=0..n, binomial(floor(n/2), floor(k/2))3^k }
MATHEMATICA
CoefficientList[Series[(1+4x-6x^2-36x^3)/(1-19x^2+90x^4), {x, 0, 40}], x] (* or *) LinearRecurrence[{0, 19, 0, -90}, {1, 4, 13, 40}, 40] (* Harvey P. Dale, Dec 24 2022 *)
CROSSREFS
Sequence in context: A379201 A034742 A149424 * A222270 A376410 A351892
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jul 25 2004
STATUS
approved