A023619 Convolution of Lucas numbers and (F(2), F(3), F(4), ...).

1, 5, 13, 29, 60, 118, 225, 419, 767, 1385, 2474, 4380, 7697, 13441, 23345, 40357, 69480, 119186, 203793, 347455, 590851, 1002385, 1696918, 2867064, 4835425, 8141693, 13687765, 22979309, 38527572, 64517230, 107915649, 180314075, 300981767, 501929081

Offset

1,2

Links

Table of n, a(n) for n=1..34.

Index entries for linear recurrences with constant coefficients, signature (2,1,-2,-1).

Formula

G.f.: x*(1+3*x+2*x^2)/(1-x-x^2)^2. - Ralf Stephan, Apr 28 2004

a(n) = (n+1)*Sum_{k=1..n+1} binomial(k,n+1-k)*(k-1)/k. - Vladimir Kruchinin, Sep 26 2011

a(n) = 2*A001629(n-1) + 3*A001629(n) + A001629(n+1). - R. J. Mathar, Oct 17 2011

a(n) = (n-1)*A000045(n) + n*A000045(n+1). - Michael Schirle, May 17 2018

Crossrefs

Sequence in context: A160430 A347503 A023617 * A020576 A093810 A093817

Adjacent sequences: A023616 A023617 A023618 * A023620 A023621 A023622

Keyword

nonn

Author

Clark Kimberling

Status

approved