A007309 - OEIS

A007309

a(n) = a(n-2) + a(n-3), with a(0) = 0, a(1) = 1, a(2) = 4.

0, 1, 4, 1, 5, 5, 6, 10, 11, 16, 21, 27, 37, 48, 64, 85, 112, 149, 197, 261, 346, 458, 607, 804, 1065, 1411, 1869, 2476, 3280, 4345, 5756, 7625, 10101, 13381, 17726, 23482, 31107, 41208, 54589, 72315, 95797, 126904, 168112, 222701, 295016, 390813, 517717, 685829, 908530

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OFFSET

0,3

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,1,1).

FORMULA

G.f.: x*(1 + 4*x)/(1 - x^2 - x^3). - Andrew Howroyd, Mar 19 2025

MATHEMATICA

LinearRecurrence[{0, 1, 1}, {0, 1, 4}, 41] (* Ray Chandler, Jul 18 2017 *)

PROG

(PARI) seq(n) = Vec((1 + 4*x)/(1 - x^2 - x^3) + O(x*x^n), -n-1) \\ Andrew Howroyd, Mar 19 2025