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

0,4

Comments

Antidiagonal sums are in A077995.

Links

Table of n, a(n) for n=0..44.

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).

Example

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,

Sequence in context: A134548 A151865 A124860 * A038138 A010704 A338947

Adjacent sequences: A182409 A182410 A182411 * A182413 A182414 A182415

Keyword

easy,nonn,tabl

Author

Philippe Deléham, Apr 27 2012

Status

approved