A362256 a(0) = a(1) = a(2) = 1, for n > 2, a(n) = a(n-1) + a(n-k) + k with k = 3.

1, 1, 1, 5, 9, 13, 17, 25, 37, 53, 73, 101, 141, 197, 273, 377, 521, 721, 997, 1377, 1901, 2625, 3625, 5005, 6909, 9537, 13165, 18173, 25085, 34625, 47793, 65969, 91057, 125685, 173481, 239453, 330513, 456201, 629685, 869141, 1199657, 1655861, 2285549, 3154693

Offset

0,4

Comments

Called Leonardo 3-numbers in the Tan-Leung paper.

Links

Table of n, a(n) for n=0..43.

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,-1,0,1,-1).

Mathematica

LinearRecurrence[{2, -1, 0, 1, -1}, {1, 1, 1, 5, 9}, 44] (* or *)
With[{p = 3}, Nest[Append[#, #[[-1]] + #[[-p - 1]] + p] &, {1, 1, 1, 5}, 40] ]

Crossrefs

Cf. A001595, A111314, A362255.

Sequence in context: A085759 A314700 A032493 * A349538 A334524 A125018

Adjacent sequences: A362253 A362254 A362255 * A362257 A362258 A362259

Keyword

nonn,easy

Author

Michael De Vlieger, Apr 13 2023

Status

approved