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A099624
a(n) = Sum_{k=0..floor(n/2)} C(n-k,k+2)*3^(n-k-2)*(4/3)^k.
1
0, 0, 1, 9, 58, 318, 1591, 7503, 33976, 149436, 643261, 2724357, 11395654, 47210154, 194121811, 793526571, 3228811492, 13090123272, 52917410041, 213437246145, 859342367890, 3455021317590, 13875655896751, 55677180731079
OFFSET
0,4
COMMENTS
In general a(n) = Sum_{k=0..floor(n/2)} C(n-k,k+2)*u^(n-k-2)*(v/u)^k has g.f. x^2/((1-u*x)^2(1-u*x-v*x^2)) and satisfies the recurrence a(n) = 3u*a(n-1)-(3u^2-v)*a(n-2)+(u^3-2uv)*a(n-3)+u^2^v*a(n-4).
FORMULA
G.f.: x^2/((1-3*x)^2*(1-3*x-4*x^2)).
a(n) = 9*a(n-1)-23*a(n-2)+3*a(n-3)+36*a(n-4).
CROSSREFS
Cf. A099623.
Sequence in context: A044528 A027174 A304370 * A018218 A026750 A009034
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 25 2004
STATUS
approved