A023549 Convolution of natural numbers >= 2 and Lucas numbers.

2, 9, 21, 43, 80, 142, 244, 411, 683, 1125, 1842, 3004, 4886, 7933, 12865, 20847, 33764, 54666, 88488, 143215, 231767, 375049, 606886, 982008, 1588970, 2571057, 4160109, 6731251, 10891448, 17622790, 28514332, 46137219, 74651651, 120788973, 195440730, 316229812

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-2,-1,1)

Crossrefs

Cf. A020701.

Programs

Mathematica

LinearRecurrence[{3, -2, -1, 1}, {2, 9, 21, 43}, 50] (* Paolo Xausa, Feb 02 2024 *)

Formula

G.f.: [x(2-x)(1+2x)]/[(1-x-x^2)(1-x)^2]. - Ralf Stephan, Apr 05 2004

a(n) = -13-3*n+5*A020701(n). - R. J. Mathar, May 22 2013