A124377 - OEIS

%I #5 Jan 12 2014 11:25:41

%S 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,

%T -2,13,-15,12,-5,1,34,12,11,-15,28,-27,17,-6,1,55,22,1,26,-43,55,-44,

%U 23,-7,1,89,33,21

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

%C 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).

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

%F 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

%F 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

%e Triangle begins

%e 1,

%e 1, 1,

%e 2, 0, 1,

%e 3, 2, -1, 1,

%e 5, 1, 3, -2, 1,

%e 8, 4, -2, 5, -3, 1,

%e 13, 4, 6, -7, 8, -4, 1,

%e 21, 9, -2, 13, -15, 12, -5, 1

%Y Cf. A000045

%K easy,sign,tabl

%O 0,4

%A _Paul Barry_, Oct 29 2006