A204040 - OEIS

A204040

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

1, 0, 1, 0, 2, 1, 0, 0, 4, 1, 0, -4, 4, 6, 1, 0, -4, -8, 12, 8, 1, 0, 4, -24, -4, 24, 10, 1, 0, 12, -8, -60, 16, 40, 12, 1, 0, 4, 56, -84, -96, 60, 60, 14, 1, 0, -20, 88, 84, -272, -100, 136, 84, 16, 1, 0, -28, -40

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OFFSET

0,5

COMMENTS

Antidiagonal sums : periodic sequence 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, ... (see A007877 or A098178).Riordan array (1, x*(1+x)/(1-x+2*x^2)) .

LINKS

Table of n, a(n) for n=0..57.

FORMULA

T(n,k) = T(n-1,k) + T(n-1,k-1) + T(n-2, k-1) - 2*T(n-2,k).

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

T(n,n) = n = A000012(n), T(n+1,n) = 2n = A005843(n), T(n+2,n) = A046092(n-1) for n>0, T(n+1,1) = A078050(n)*(-1)^n.

Sum_{k, 0<=k<=n} T(n,k) = A060747(n) = A005408(n-1).