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A073372 Second convolution of A001045(n+1) (generalized (1,2)-Fibonacci), n>=0, with itself. 5
1, 3, 12, 34, 99, 261, 678, 1692, 4149, 9959, 23568, 55014, 127031, 290457, 658602, 1482240, 3314025, 7365915, 16285300, 35832810, 78500811, 171293293, 372412782, 806963364, 1743173469, 3754782351, 8066319768, 17285917742, 36957928479, 78847115649 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..29.

FORMULA

a(n) = sum(b(k)*c(n-k), k=0..n) with b(k) := A001045(k+1) and c(k) := A073371(k).

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

a(n) = ((30+9*n)*(n+1)*U(n+1)+2*(33+9*n)*(n+2)*U(n))/(2*9^2) with U(n) := A001045(n+1), n>=0.

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

MATHEMATICA

CoefficientList[Series[-(-1+x+2x^2)^(-3), {x, 0, 78}], x] (* or *) Table[(-3*(-1)^n*n^2+3*2^(n+2)*n^2-15*(-1)^n*n+9*2^(n+2)*n-16*(-1)^n+2^(n+4))/162, {n, 42}] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2012 *)

CROSSREFS

Third (m=2) column of triangle A073370.

Sequence in context: A060298 A304975 A226546 * A305023 A026573 A225075

Adjacent sequences:  A073369 A073370 A073371 * A073373 A073374 A073375

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Aug 02 2002

STATUS

approved

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Last modified April 26 12:07 EDT 2019. Contains 322472 sequences. (Running on oeis4.)