0,21

Number of partitions of n into parts 9, 10, and 11. - Hoang Xuan Thanh, Sep 28 2025

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

a(n) = a(n-9) + a(n-10) + a(n-11) - a(n-19) - a(n-20) - a(n-21) + a(n-30). - R. J. Mathar, Jul 19 2014

a(n) = floor((n^2+30*n+1820)/1980 + ((2*n^2+6*n+4) mod 9)/9 - (n mod 10)*(10-(n mod 10))/20). - Hoang Xuan Thanh, Sep 28 2025

CoefficientList[1/Series[Times@@(1-x^Range[9, 11]), {x, 0, 120}], x] (* or *) LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 1, 0, 0, 0, 0, 1, 1, 2}, 120] (* Harvey P. Dale, Apr 01 2018 *)

(PARI) Vec(1/((1-x^9)*(1-x^10)*(1-x^11)) + O(x^90)) \\ Jinyuan Wang, Feb 28 2020

(PARI) a(n) = (n^2+30*n+1820)/1980 + ((2*n^2+6*n+4)%9)/9 - ((3*n^2+2*n+4)%11)/11 - (n%10)*(10-(n%10))/20 \\ Hoang Xuan Thanh, Sep 28 2025

Sequence in context: A127326 A321923 A064663 * A351358 A138158 A057276

Adjacent sequences: A025920 A025921 A025922 * A025924 A025925 A025926

nonn,easy

approved