A029000 Expansion of 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^6)).

1, 1, 2, 3, 4, 5, 8, 9, 12, 15, 18, 21, 27, 30, 36, 42, 48, 54, 64, 70, 80, 90, 100, 110, 125, 135, 150, 165, 180, 195, 216, 231, 252, 273, 294, 315, 343, 364, 392, 420, 448, 476, 512, 540, 576, 612, 648, 684, 729, 765, 810, 855, 900, 945, 1000, 1045, 1100

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Number of partitions of n into parts 1, 2, 3, and 6. - Joerg Arndt, Jul 04 2013

Links

• Index entries for linear recurrences with constant coefficients, signature (1,1,0,-1,-1,2,-1,-1,0,1,1,-1).

Programs

Magma

[Floor(1/18*(-3*Floor((n + 2)/3) + 3*Floor(n/3) + 2)*(Floor(n/3) + 1) + 1/432*(n + 6)*(2*n^2 + 24*n + 47+9*(-1)^n) + 7/36): n in [0..80]]; // Vincenzo Librandi, May 12 2015

Mathematica

CoefficientList[Series[1/((1 - x) (1 - x^2) (1 - x^3) (1 - x^6)), {x, 0, 80}], x] (* Vincenzo Librandi, May 12 2015 *)

PARI

Vec(1/((1-x)*(1-x^2)*(1-x^3)*(1-x^6))+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012

Formula

a(n) = floor((1/18)*(-3*floor((n + 2)/3) + 3*floor(n/3) + 2)*(floor(n/3) + 1) + (1/432)*(n + 6)*(2*n^2 + 24*n + 47+9*(-1)^n) + 7/36). - Tani Akinari, Jul 04 2013

a(n) = 1 + floor((2*n^3 + 36*n^2 + 183*n + 24*n*[(n mod 3)=0] + 9*n*(-1)^n)/432) where [] is Iverson bracket. - Hoang Xuan Thanh, Jun 10 2025

Extensions

More terms from Vincenzo Librandi, May 12 2015