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A073373 Third convolution of A001045(n+1) (generalized (1,2)-Fibonacci), n>=0, with itself. 1
1, 4, 18, 60, 195, 576, 1644, 4488, 11925, 30860, 78278, 195012, 478599, 1159080, 2774880, 6575280, 15439065, 35955540, 83118970, 190862860, 435601611, 988620624, 2232236628, 5016441240, 11224087965 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (4,2,-20,-1,40,8,-32,-16).

FORMULA

a(n) = sum(b(k) * c(n-k), k=0..n) with b(k) := A001045(k+1) and c(k) := A073372(k).

a(n) = sum(binomial(n-k+3, 3) * binomial(n-k, k) * 2^k, k=0..floor(n/2)).

a(n) = ((350+177*n+21*n^2)*(n+1)*U(n+1)+2*(277+132*n+15*n^2)*(n+2)*U(n))/ (2*9^3) with U(n) := A001045(n+1), n>=0.

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

CROSSREFS

Fourth (m=3) column of triangle A073370.

Sequence in context: A212521 A278406 A192069 * A292465 A227162 A057414

Adjacent sequences:  A073370 A073371 A073372 * A073374 A073375 A073376

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Aug 02 2002

STATUS

approved

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Last modified April 19 19:09 EDT 2019. Contains 322290 sequences. (Running on oeis4.)