A029073 Expansion of 1/((1-x)*(1-x^4)*(1-x^7)*(1-x^8)).

1, 1, 1, 1, 2, 2, 2, 3, 5, 5, 5, 6, 8, 8, 9, 11, 14, 14, 15, 17, 20, 21, 23, 26, 30, 31, 33, 36, 41, 43, 46, 50, 56, 58, 61, 66, 73, 76, 80, 86, 94, 97, 102, 109, 118, 122, 128, 136, 146, 151, 158, 167, 178, 184, 192

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Number of partitions of n into parts 1, 4, 7 and 8. - Ilya Gutkovskiy, May 18 2017

References

• J. C. P. Miller, On the enumeration of partially ordered sets of integers, pp. 109-124 of T. P. McDonough and V. C. Mavron, editors, Combinatorics: Proceedings of the Fourth British Combinatorial Conference 1973. London Mathematical Society, Lecture Note Series, Number 13, Cambridge University Press, NY, 1974. The g.f. is G_{rot}(t) on page 122.

Links

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

Programs

Maple

1/( (1-x)*(1-x^4)*(1-x^7)*(1-x^8) );

PARI

a(n) = floor((n^3 + 30*n^2 + 257*n + 1344)/1344 + (n/64)*[3,0,-1,0][n%4+1] + (3/7)*((n%8==0) - (n%28==6) - (n%28==27))) \\ Hoang Xuan Thanh, Aug 01 2025

Formula

a(n) = floor((n^3 + 30*n^2 + 257*n + 1344)/1344 + ((n+7)/64)*(3*[(n mod 4)=0] - [(n mod 4)=2]) + (1/7)*([(n mod 56)=16] - [(n mod 56)=27])). - Hoang Xuan Thanh, Aug 01 2025