|
%I
%S 1,1,-1,1,0,1,1,1,1,-1,1,2,2,0,1,1,3,4,2,1,-1,1,4,7,6,3,0,1,1,5,11,13,
%T 9,3,1,-1,1,6,16,24,22,12,4,0,1,1,7,22,40,46,34,16,4,1,-1,1,8,29,62,
%U 86,80,50,20,5,0,1,1,9,37,91,148,166,130,70,25,5,1,-1,1,10,46,128,239,314,296,200,95,30,6,0,1,1,11,56,174,367
%N Triangle read by rows: T(n,0)=1, T(n,n)=(-1)^floor(n/2), T(n+1,k)=T(n,k-1)+T(n,k) for 0<k<n.
%C Sum(T(n,k): 0<=k<=n) = A078008(n);
%C Sum(abs(T(n,k)): 0<=k<=n) = A052953(n-1) for n>0;
%C T(n,1) = n - 2 for n>1;
%C T(n,2) = A000124(n-3) for n>2;
%C T(n,3) = A003600(n-4) for n>4;
%C T(n,n-6) = A001753(n-6) for n>6;
%C T(n,n-5) = A001752(n-5) for n>5;
%C T(n,n-4) = A002623(n-4) for n>4;
%C T(n,n-3) = A002620(n-1) for n>3;
%C T(n,n-2) = A008619(n-2) for n>2;
%C T(n,n-1) = n mod 2 for n>0;
%C T(2*n,n) = A072547(n+1).
%H <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>
%t Clear[t]; t[n_, 0] = 1; t[n_, n_] := t[n, n] = (-1)^Mod[n, 2]; t[n_, k_] := t[n, k] = t[n-1, k] + t[n-1, k-1]; Table[t[n, k], {n, 0, 13}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Mar 06 2013 *)
%Y Cf. A007318.
%Y Similar to the triangles A035317, A059259, A080242, A112555.
%K sign,tabl
%O 0,12
%A _Reinhard Zumkeller_, Jun 10 2005
|
