A112476 Diagonal sums of Riordan array (1/(1+x),x(1+x)/(1-x)).

1, -1, 2, 0, 3, 3, 8, 12, 25, 43, 82, 148, 275, 503, 928, 1704, 3137, 5767, 10610, 19512, 35891, 66011, 121416, 223316, 410745, 755475, 1389538, 2555756, 4700771, 8646063, 15902592, 29249424, 53798081, 98950095, 181997602, 334745776, 615693475, 1132436851, 2082876104, 3831006428

Offset: 0

Author

Paul Barry, Sep 07 2005

Keywords

• easy
• sign

Comments

Diagonal sums of A112475.

Links

• Index entries for linear recurrences with constant coefficients, signature (0,2,2,1).

Formula

G.f.: (1-x)/((1+x)*(1-x-x^2-x^3)).

a(n) = 2*a(n-2)+2*a(n-3)+a(n-4).

a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..n-2*k} C(k-1, j)*C(n-k-j-1, n-2*k-j).