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

Author

Clark Kimberling

Keywords

• nonn

Links

• 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