A025813 - OEIS

%I #13 Jun 30 2026 22:11:25

%S 1,0,1,0,1,0,2,1,2,1,2,1,3,2,4,2,4,2,5,3,6,4,6,4,7,5,8,6,9,6,10,7,11,

%T 8,12,9,13,10,14,11,15,12,17,13,18,14,19,15,21,17,22,18,23,19,25,21,

%U 27,22,28,23,30,25,32,27,33

%N Expansion of 1/((1-x^2)*(1-x^6)*(1-x^7)).

%C Number of partitions of n into parts 2, 6, and 7. - _Hoang Xuan Thanh_, Aug 29 2025

%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,0,0,1,1,-1,-1,0,0,0,-1,0,1).

%F a(n) = floor((n^2 + 15*n + 7*(n+8)*(-1)^n + 119)/168). - _Hoang Xuan Thanh_, Aug 29 2025

%t CoefficientList[Series[1/((1-x^2)(1-x^6)(1-x^7)),{x,0,70}],x] (* _Harvey P. Dale_, Nov 06 2017 *)

%t (* Alternative: *)

%t LinearRecurrence[{0,1,0,0,0,1,1,-1,-1,0,0,0,-1,0,1},{1,0,1,0,1,0,2,1,2,1,2,1,3,2,4},70] (* _Harvey P. Dale_, Nov 06 2017 *)

%o (PARI) a(n) = (n^2 + 15*n + 7*(n+8)*(-1)^n + 119)\168 \\ _Hoang Xuan Thanh_, Aug 29 2025

%K nonn,easy,changed

%O 0,7

%A _N. J. A. Sloane_