A182412 Triangle T(n,k), read by rows, given by (1, 2, -2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 2, -1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

1, 1, 1, 3, 6, 3, 5, 17, 19, 7, 11, 48, 80, 60, 17, 21, 119, 270, 308, 177, 41, 43, 290, 823, 1256, 1087, 506, 99, 85, 677, 2321, 4447, 5147, 3601, 1411, 239, 171, 1556, 6234, 14360, 20806, 19424, 11416, 3864, 577

Offset: 0

Author

Philippe Deléham, Apr 27 2012

Keywords

• easy
• nonn
• tabl

Comments

Antidiagonal sums are in A077995.

Examples

			Triangle begins
1
1, 1
3, 6, 3
5, 17, 19, 7
11, 48, 80, 60, 17
21, 119, 270, 308, 177, 41
43, 290, 823, 1256, 1087, 506, 99
85, 677, 2321, 4447, 5147, 3601, 1411, 239
		

Crossrefs

Cf. A001045, A001333, A077995,

Formula

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

T(n,k) = T(n-1,k) + 2*T(n-1,k-1) + 2*T(n-2,k) + 3*T(n-2,k-1) + T(n-2,k-2), T(0,0) = T(1,0) = T(1,1) = 1, T(2,0) = T(2,2) = 3, T(2,1) = 6 and T(n,k) = 0 if k<0 or if k>n.

T(n,n) = A001333(n), T(n,0) = A001045(n+1).

Sum_{k, 0<=k<=n} T(n,k)*(-1)^k = A000007(n).