VOOZH about

URL: https://oeis.org/A025898

⇱ A025898 - OEIS

login
A025898
Expansion of 1/((1-x^6)*(1-x^7)*(1-x^9)).
6
1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 2, 1, 1, 2, 1, 1, 2, 2, 1, 3, 2, 1, 3, 2, 2, 3, 3, 2, 4, 3, 2, 4, 3, 3, 5, 4, 3, 5, 4, 3, 6, 5, 4, 6, 5, 4, 7, 6, 5, 7, 6, 5, 8, 7, 6, 9, 7, 6, 9, 8, 7, 10, 9, 7, 11, 9, 8, 11, 10, 9, 12
OFFSET
0,19
COMMENTS
a(n) is the number of partitions of n into parts 6, 7, and 9. - Joerg Arndt, Jan 23 2024
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1,1,0,1,0,0,0,-1,0,-1,-1,0,0,0,0,0,1).
FORMULA
a(n) = floor((n^2+36*n+324)/756 - n*(n mod 3)/54 + ((2*n^2+2*n+4) mod 7)/7). - Hoang Xuan Thanh, Sep 24 2025
MATHEMATICA
CoefficientList[Series[1/((1-x^6)*(1-x^7)*(1-x^9)), {x, 0, 100}], x] (* G. C. Greubel, Jan 22 2024 *)
LinearRecurrence[{0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, -1, 0, -1, -1, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 2, 1, 1, 2}, 80] (* Harvey P. Dale, Jun 18 2025 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 100); Coefficients(R!( 1/((1-x^6)*(1-x^7)*(1-x^9)) )); // G. C. Greubel, Jan 22 2024
(SageMath)
def A025898_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/((1-x^6)*(1-x^7)*(1-x^9)) ).list()
A025898_list(100) # G. C. Greubel, Jan 22 2024
(PARI) a(n) = (n^2+36*n+324 - 14*n*(n%3) + 108*((2*n^2+2*n+4)%7))\756 \\ Hoang Xuan Thanh, Sep 24 2025
KEYWORD
nonn,easy
STATUS
approved