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A073388 Convolution of A002605(n) (generalized (2,2)-Fibonacci), n >= 0, with itself. 8
1, 4, 16, 56, 188, 608, 1920, 5952, 18192, 54976, 164608, 489088, 1443776, 4238336, 12382208, 36022272, 104407296, 301618176, 868765696, 2495715328, 7152286720, 20452548608, 58369409024 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Muniru A Asiru, Table of n, a(n) for n = 0..500

FORMULA

a(n) = Sum_{k=0..n} (b(k)*b(n-k) with b(k) := A002605(k).

a(n) = (2^n)*Sum_{k=0..floor(n/2)} binomial(n-k+1, 1)*binomial(n-k, k)*(1/2)^k.

a(n) = ((n+1)*U(n+1) + 2*(n+2)*U(n))/6, with U(n) := A002605(n), n >= 0.

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

a(n) = Sum_{k=0..floor((n+2)/2)} k*binomial(n-k+2, k)2^(n-k+1). - Paul Barry, Oct 15 2004

PROG

(Sage) taylor( mul(x/(1 - 2*x - 2*x^2) for i in xrange(1, 3)), x, 0, 24) # Zerinvary Lajos, Jun 03 2009

(GAP) List([0..25], n->2^n*Sum([0..Int(n/2)], k->Binomial(n-k+1, 1)*Binomial(n-k, k)*(1/2)^k)); # Muniru A Asiru, Jun 12 2018

CROSSREFS

Second (m=1) column of triangle A073387.

Sequence in context: A239988 A308288 A261386 * A109634 A026126 A026155

Adjacent sequences:  A073385 A073386 A073387 * A073389 A073390 A073391

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Aug 02 2002

STATUS

approved

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Last modified October 21 01:18 EDT 2019. Contains 328291 sequences. (Running on oeis4.)