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A073390 Third convolution of A002605(n) (generalized (2,2)-Fibonacci), n >= 0, with itself. 2
1, 8, 48, 240, 1080, 4512, 17856, 67776, 248880, 889600, 3109376, 10664448, 35989248, 119761920, 393676800, 1280157696, 4122985728, 13165099008, 41713192960, 131243970560, 410315433984, 1275348344832 (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)*c(n-k) with b(k) := A002605(k) and c(k) := A073389(k).

a(n) = (2^n)*Sum_{k=0..floor(n/2)} binomial(n-k+3, 3)*binomial(n-k, k)*(1/2)^k.

a(n) = ((64 + 37*n + 5*n^2)*(n+1)*U(n+1) + 4*(11 + 7*n + n^2)*(n+2)*U(n))/(6^3), with U(n) := A002605(n), n >= 0.

G.f.: 1/(1-2*x*(1+x))^4.

PROG

(GAP) List([0..25], n->2^n*Sum([0..Int(n/2)], k->Binomial(n-k+3, 3)*Binomial(n-k, k)*(1/2)^k)); # Muniru A Asiru, Jun 12 2018

CROSSREFS

Fourth (m=3) column of triangle A073387.

Cf. A002605, A073389.

Sequence in context: A211012 A081084 A230931 * A069021 A079763 A079785

Adjacent sequences:  A073387 A073388 A073389 * A073391 A073392 A073393

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Aug 02 2002

STATUS

approved

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Last modified August 22 02:44 EDT 2019. Contains 326169 sequences. (Running on oeis4.)