A393384 - OEIS

%I #4 Feb 15 2026 23:29:05

%S 1,3,5,11,17,23,33,43,53,75,97,119,153,187,221,267,313,359,425,491,

%T 557,643,729,815,921,1027,1133,1283,1433,1583,1777,1971,2165,2403,

%U 2641,2879,3185,3491,3797,4171,4545,4919,5361,5803,6245,6779,7313,7847,8473

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

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

%t a[0] = 1; a[n_] := a[n] = a[n - 1] + 2 a[Floor[n/3]]; Table[a[n], {n, 0, 48}]

%t 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]

%Y Cf. A005704, A058039, A393382.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Feb 13 2026