OFFSET
0,4
COMMENTS
Column 0 equals (essentially) column 1 and the rightmost border.
FORMULA
EXAMPLE
Triangle begins:
1;
1, 1, 2;
2, 2, 3, 4, 6;
6, 6, 8, 10, 13, 17, 23;
23, 23, 29, 35, 43, 53, 66, 83, 106;
106, 106, 129, 152, 181, 216, 259, 312, 378, 461, 567;
567, 567, 673, 779, 908, 1060, 1241, 1457, 1716, 2028, 2406, 2867, 3434; ...
MATHEMATICA
t[n_, k_] := t[n, k] = t[n, k-1] + t[n-1, k-2]; t[n_, 0] := t[n, 0] = t[n-1, 2n-2]; t[n_, 1] := t[n, 0]; t[0, 0] = 1; Flatten[ Table[t[n, k], {n, 0, 7}, {k, 0, 2 n}]] (* Jean-François Alcover, Jun 18 2012 *)
PROG
(PARI) T(n, k)=local(A=[1]); if(2*n<k || k<0, 0, if(n==0 && k==0, 1, if(k==0 || k==1, T(n-1, 2*n-2), for(i=1, n, A=Vec(Ser(concat([A[ #A], 0], A))/(1-x))); A[k+1])))
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Paul D. Hanna, Aug 21 2007
STATUS
approved