A124377 - OEIS

A124377

Riordan array (1/(1-x-x^2),x/(1+x)).

1, 1, 1, 2, 0, 1, 3, 2, -1, 1, 5, 1, 3, -2, 1, 8, 4, -2, 5, -3, 1, 13, 4, 6, -7, 8, -4, 1, 21, 9, -2, 13, -15, 12, -5, 1, 34, 12, 11, -15, 28, -27, 17, -6, 1, 55, 22, 1, 26, -43, 55, -44, 23, -7, 1, 89, 33, 21

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OFFSET

0,4

COMMENTS

First column is F(n+1). Second column is A008346. Row sums are F(n+2). Diagonal sums are A094966(n+1). Product of A007318 and A124377 is the Riordan array ((1-x)/(1-3x+x^2),x), the sequence array for F(2n+1).

LINKS

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

FORMULA

Number triangle T(n,k)=sum{j=0..n-k, C(j-k,n-k-j)}*[k<=n]

T(n,k)=T(n-1,k-1)+2*T(n-2,k)-T(n-2,k-1)+T(n-3,k)-T(n-3,k-1), T(0,0)=T(1,0)=T(1,1)=1, T(n,k)=0 if k<0 or if k>n. - Philippe Deléham, Jan 12 2014

T(n,0)=A000045(n+1), T(n,n)=1, T(n,k)=T(n-1,k-1)-T(n-1,k) for 0<k<n. - Philippe Deléham, Jan 12 2014

EXAMPLE

Triangle begins

1, 1,

2, 0, 1,

3, 2, -1, 1,

5, 1, 3, -2, 1,