A362255 - OEIS

A362255

a(0) = a(1) = a(2) = 1, for n > 2, a(n) = a(n-1) + a(n-k) + k with k = 2.

1, 1, 1, 4, 7, 10, 16, 25, 37, 55, 82, 121, 178, 262, 385, 565, 829, 1216, 1783, 2614, 3832, 5617, 8233, 12067, 17686, 25921, 37990, 55678, 81601, 119593, 175273, 256876, 376471, 551746, 808624, 1185097, 1736845, 2545471, 3730570, 5467417, 8012890, 11743462, 17210881

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OFFSET

0,4

COMMENTS

Called Leonardo 2-numbers in the Tan-Leung paper.

LINKS

Table of n, a(n) for n=0..42.

Elif Tan and Ho-Hon Leung, On Leonardo p-Numbers, Integers (2023) Vol. 23, #A7. See p. 2.

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

MATHEMATICA

LinearRecurrence[{2, -1, 1, -1}, {1, 1, 1, 4}, 40] (* or *)

With[{k = 2}, Nest[Append[#, #[[-1]] + #[[-k - 1]] + k] &, {1, 1, 1}, 40] ]