A391995 - OEIS

%I #13 Jan 10 2026 07:21:20

%S 0,0,-1,-1,-1,1,4,10,18,30,45,65,89,119,154,196,244,300,363,435,515,

%T 605,704,814,934,1066,1209,1365,1533,1715,1910,2120,2344,2584,2839,

%U 3111,3399,3705,4028,4370,4730,5110,5509,5929,6369,6831,7314,7820,8348,8900,9475

%N a(n) = (4*n^3 - 18*n^2 - 4*n + 9*(1 - (-1)^n)) / 48.

%F gf(k) = (2*a(k)*x^2 - A212964(k)*x)/(x^3 - 3*x^2 + 3*x - 1) is the g.f. of row k of A392248.

%p a := n -> (4*n^3 - 18*n^2 - 4*n + 9*(1-(-1)^n))/48: seq(a(n), n = 0..50);

%t LinearRecurrence[{3, -2, -2, 3, -1}, {0, 0, -1, -1, -1}, 50] (* _Hugo Pfoertner_, Jan 09 2026 *)

%Y Cf. A212964, A392248.

%K sign,easy

%O 0,7

%A _Peter Luschny_, Jan 09 2026