A182412 - OEIS

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

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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

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