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

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).

Formula

From Elmo R. Oliveira, Apr 01 2026: (Start)

G.f.: (2*x^3 - x + 1)/((x^3 + x - 1)*(x - 1)).

a(n) = 2*a(n-1) - a(n-2) + a(n-3) - a(n-4). (End)

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] ]

Crossrefs

Cf. A001595, A111314, A362256.

Sequence in context: A180080 A153003 A213484 * A128429 A191154 A209257

Adjacent sequences: A362252 A362253 A362254 * A362256 A362257 A362258

Keyword

nonn,easy

Author

Michael De Vlieger, Apr 13 2023

Status

approved