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A099583 a(n) = Sum_{k=0..floor(n/2)} binomial(n-k, k-1)*2^(n-k-1)*(3/2)^(k-1). 0
0, 0, 1, 2, 10, 26, 91, 260, 820, 2420, 7381, 22022, 66430, 198926, 597871, 1792520, 5380840, 16139240, 48427561, 145272842, 435848050, 1307514626, 3922632451, 11767808780, 35303692060, 105910810460, 317733228541, 953198888462 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

In general, a(n) = Sum_{k=0..floor(n/2)} binomial(n-k, k-1)*u^(n-k-1)*(v/u)^(k-1) has g.f. x^2/((1-v*x^2)(1-u*x-v*x^2)) and satisfies the recurrence a(n) = u*a(n-1) + 2v*a(n-2) - u*v*a(n-3) - v^2*a(n-4).

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (2,6,-6,-9).

FORMULA

G.f.: x^2/((1-3*x^2)*(1-2*x-3*x^2)).

a(n) = 2*a(n-1) + 6*a(n-2) - 6*a(n-3) - 9*a(n-4).

a(n) = A002452(n/2) if n even; a(n) = 2*A006100((n+1)/2) if n odd. - R. J. Mathar, Jun 06 2010

a(0)=0, a(1)=0; a(2)=1; a(n) = 2*a(n-1) + 3*a(n-2) if n is odd; a(n) = 2*a(n-1) + 3*a(n-2) + 3^m (m=1,2,3...) if n is even. - Vincenzo Librandi, Jun 26 2010

PROG

(PARI) a(n) = sum(k=0, n\2, binomial(n-k, k-1)*2^(n-k-1)*(3/2)^(k-1)); \\ Michel Marcus, Jan 20 2018

CROSSREFS

Cf. A006100, A002452.

Sequence in context: A084182 A321240 A322201 * A133479 A196324 A196648

Adjacent sequences:  A099580 A099581 A099582 * A099584 A099585 A099586

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Oct 23 2004

STATUS

approved

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Last modified March 19 17:21 EDT 2019. Contains 321330 sequences. (Running on oeis4.)