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A099625 Sum C(n-k,k+2)2^(n-k-2)(1/2)^k, k=0..floor(n/2). 1
0, 0, 1, 6, 25, 88, 281, 842, 2413, 6692, 18101, 48014, 125393, 323376, 825393, 2088850, 5248853, 13110844, 32584653, 80639446, 198844281, 488813768, 1198491913, 2931934938, 7158830781, 17450923092, 42480107365, 103283553054 (list; graph; refs; listen; history; text; internal format)
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).

LINKS

Table of n, a(n) for n=0..27.

Index entries for linear recurrences with constant coefficients, signature (6,-11,4,4).

FORMULA

G.f.: x^2/((1-2x)^2(1-2x-x^2)); a(n)=sum{k=0..floor(n/2), C(n-k, k+2)2^(n-2k-2)}; a(n)=6a(n-1)-11a(n-2)+4a(n-3)+4a(n-4).

CROSSREFS

Cf. A099623, A099624.

Sequence in context: A230723 A220275 A055585 * A209243 A143628 A056279

Adjacent sequences:  A099622 A099623 A099624 * A099626 A099627 A099628

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Oct 25 2004

STATUS

approved

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Last modified May 22 00:25 EDT 2019. Contains 323472 sequences. (Running on oeis4.)