A393384 a(0) = 1; a(n) = a(n-1) + 2 * a(floor(n/3)).

1, 3, 5, 11, 17, 23, 33, 43, 53, 75, 97, 119, 153, 187, 221, 267, 313, 359, 425, 491, 557, 643, 729, 815, 921, 1027, 1133, 1283, 1433, 1583, 1777, 1971, 2165, 2403, 2641, 2879, 3185, 3491, 3797, 4171, 4545, 4919, 5361, 5803, 6245, 6779, 7313, 7847, 8473

Offset

0,2

Links

Table of n, a(n) for n=0..48.

Formula

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

Mathematica

a[0] = 1; a[n_] := a[n] = a[n - 1] + 2 a[Floor[n/3]]; Table[a[n], {n, 0, 48}]
nmax = 48; A[_] = 1; Do[A[x_] = (2 (1 + x + x^2) A[x^3] - 1)/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Crossrefs

Cf. A005704, A058039, A393382.

Sequence in context: A106902 A343048 A293711 * A155938 A158318 A099596

Adjacent sequences: A393381 A393382 A393383 * A393385 A393386 A393387

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 13 2026

Status

approved