cp's OEIS Frontend

A288267 Triangle read by rows: T(n,k) = T(n,k+1) + T(n-k,k-1) with T(0,0) = 1 and T(n,k) = 0 if k<0 or k > A003056(n).

%I A288267 #32 Nov 14 2020 07:58:08
%S A288267 1,1,1,1,1,2,2,1,3,3,1,5,5,2,9,9,4,1,15,15,6,1,26,26,11,2,45,45,19,4,
%T A288267 78,78,33,7,1,135,135,57,12,1,234,234,99,21,2,406,406,172,37,4,704,
%U A288267 704,298,64,7,1222,1222,518,112,13,1,2120,2120,898,194,22,1,3679
%N A288267 Triangle read by rows: T(n,k) = T(n,k+1) + T(n-k,k-1) with T(0,0) = 1 and T(n,k) = 0 if k<0 or k > A003056(n).
%H A288267 Seiichi Manyama, <a href="/A288267/b288267.txt">Rows n = 0..481, flattened</a>
%e A288267 First few rows are:
%e A288267    1;
%e A288267    1,  1;
%e A288267    1,  1;
%e A288267    2,  2, 1;
%e A288267    3,  3, 1;
%e A288267    5,  5, 2;
%e A288267    9,  9, 4, 1;
%e A288267   15, 15, 6, 1.
%p A288267 T:= proc(n,k) option remember; `if`(k<0 or k*(k+1)/2>n, 0,
%p A288267       `if`(n=0, 1, T(n, k+1)+T(n-k, k-1)))
%p A288267     end:
%p A288267 seq(seq(T(n, k), k=0..floor((sqrt(1+8*n)-1)/2)), n=0..20); # _Alois P. Heinz_, Sep 01 2017
%t A288267 T[n_, k_] := T[n, k] = If[k < 0 || k(k+1)/2 > n, 0, If[n == 0, 1, T[n, k+1] + T[n-k, k-1]]];
%t A288267 Table[T[n, k], {n, 0, 20}, {k, 0, Floor[(Sqrt[8n+1]-1)/2]}] // Flatten (* _Jean-François Alcover_, Nov 14 2020, after _Alois P. Heinz_ *)
%Y A288267 Columns 0+1,2 give A005169, A289080 (for n>0).
%Y A288267 Cf. A003056.
%K A288267 nonn,tabf
%O A288267 0,6
%A A288267 _Seiichi Manyama_, Sep 01 2017