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

1,1

Links

Table of n, a(n) for n=1..36.

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

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

Mathematica

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

Crossrefs

Cf. A020701.

Sequence in context: A005476 A316430 A131476 * A192971 A024850 A237044

Adjacent sequences: A023546 A023547 A023548 * A023550 A023551 A023552

Keyword

nonn

Author

Clark Kimberling

Status

approved