cp's OEIS Frontend

A132289 Triangle, read by rows of 2n+1 terms, where T(n,k) = T(n,k-1) + T(n-1,k-1) for 2n>=k>0, T(n,2n-1) = T(n,2n-2) + T(n-1,n-1) and T(n,2n) = T(n,2n-1) + T(n-1,n-1) for n>0, with T(n,0) = T(n-1,n-1) for n>0 and T(0,0) = 1.

%I A132289 #11 Sep 22 2024 17:55:24
%S A132289 1,1,2,3,3,4,6,9,12,12,15,19,25,34,46,58,58,70,85,104,129,163,209,267,
%T A132289 325,325,383,453,538,642,771,934,1143,1410,1735,2060,2060,2385,2768,
%U A132289 3221,3759,4401,5172,6106,7249,8659,10394,12454,14514,14514,16574,18959
%N A132289 Triangle, read by rows of 2n+1 terms, where T(n,k) = T(n,k-1) + T(n-1,k-1) for 2n>=k>0, T(n,2n-1) = T(n,2n-2) + T(n-1,n-1) and T(n,2n) = T(n,2n-1) + T(n-1,n-1) for n>0, with T(n,0) = T(n-1,n-1) for n>0 and T(0,0) = 1.
%C A132289 Column 0 and the rightmost border (shifted right) equal A125276.
%e A132289 Triangle begins:
%e A132289   1;
%e A132289   1, 2, 3;
%e A132289   3, 4, 6, 9, 12;
%e A132289   12, 15, 19, 25, 34, 46, 58;
%e A132289   58, 70, 85, 104, 129, 163, 209, 267, 325;
%e A132289   325, 383, 453, 538, 642, 771, 934, 1143, 1410, 1735, 2060;
%e A132289   2060, 2385, 2768, 3221, 3759, 4401, 5172, 6106, 7249, 8659, 10394, 12454, 14514; ...
%o A132289 (PARI) T(n,k)=my(A=[1]);if(2*n<k || k<0,0,if(n==0,1,for(i=1,n, A=Vec(Ser(concat(concat(A[ #A],A),A[ #A]))/(1-x)));A[k+1]))
%Y A132289 Cf. A132290 (main diagonal), A125276 (column 0).
%K A132289 nonn,tabf
%O A132289 0,3
%A A132289 _Paul D. Hanna_, Aug 18 2007