A391264 a(3*n) = 1, a(3*n+1) = 3*n+1, a(3*n+2) = (3*n+1)*(3*n+2)/2.

1, 1, 1, 1, 4, 10, 1, 7, 28, 1, 10, 55, 1, 13, 91, 1, 16, 136, 1, 19, 190, 1, 22, 253, 1, 25, 325, 1, 28, 406, 1, 31, 496, 1, 34, 595, 1, 37, 703, 1, 40, 820, 1, 43, 946, 1, 46, 1081, 1, 49, 1225, 1, 52, 1378, 1, 55, 1540, 1, 58, 1711, 1, 61, 1891, 1, 64, 2080

Offset

0,5

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (0,0,3,0,0,-3,0,0,1).

Formula

G.f.: (1+x+x^2-2*x^3+x^4+7*x^5+x^6-2*x^7+x^8)/(1-x^3)^3.

E.g.f.: (1+x+x^2/2)*(exp(x)+exp(w*x)+exp(w^2*x))/3, w=exp(2*Pi*I/3).

Mathematica

A391264[n_] := Switch[Mod[n, 3], 0, 1, 1, n, _, n*(n-1)/2];
Array[A391264, 100, 0] (* Paolo Xausa, Jan 22 2026 *)

Crossrefs

Trisections give: A000012, A016777, A060544.

Sequence in context: A008345 A279082 A016488 * A087212 A048870 A337840

Adjacent sequences: A391261 A391262 A391263 * A391265 A391266 A391267

Keyword

nonn,easy

Author

Paul Barry, Jan 09 2026

Status

approved