A236771 a(n) = n + floor(n/2 + n^2/3).

0, 1, 4, 7, 11, 15, 21, 26, 33, 40, 48, 56, 66, 75, 86, 97, 109, 121, 135, 148, 163, 178, 194, 210, 228, 245, 264, 283, 303, 323, 345, 366, 389, 412, 436, 460, 486, 511, 538, 565, 593, 621, 651, 680, 711, 742, 774, 806, 840, 873, 908, 943, 979

Offset: 0

Author

Bruno Berselli, Feb 06 2014

Keywords

• nonn
• easy

Comments

If a(k) is prime then k == 3, 4 or 8 (mod 12). The primes are 7, 11, 97, 109, 163, 283, 389, 593, 1129, 1987, 2039, 2713, ... .

This sequence is between A042965 and A236773.

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,0,-1,-1,1).

Crossrefs

Cf. A004772; A032766: n+floor(n/2).

Cf. A042965: n+floor(1/2+n/3); A236773: n+floor(n^2/2+n^3/3).

Cf. A281333: 1+floor(n/2)+floor(n^2/3).

Programs

Magma

[n+Floor(n/2+n^2/3): n in [0..60]];

Mathematica

Table[n + Floor[n/2 + n^2/3], {n, 0, 60}]

Formula

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

a(n) = a(n-1) + a(n-2) - a(n-4) - a(n-5) + a(n-6).

a(n) = (2*n*(2*n+9) - 2*(-1)^floor(2*(n-1)/3) + 3*(-1)^n - 5)/12.

a(n+2) - a(n) = A004772(n+4).

Also: a(n) = n + floor(n/2) + floor(n^2/3).