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A110570 Triangle read by rows: T(n,0) = T(n,n) = 1 and for 0 T(n,k) = if k<=n/2 then T(n-k,0)+T(n-k,k) else T(k,n-k)+T(k,n).

%I A110570 #10 Aug 31 2017 23:02:09
%S A110570 1,1,1,1,2,1,1,3,3,1,1,4,2,4,1,1,5,4,4,5,1,1,6,3,2,3,6,1,1,7,5,5,5,5,
%T A110570 7,1,1,8,4,5,2,5,4,8,1,1,9,6,3,6,6,3,6,9,1,1,10,5,6,4,2,4,6,5,10,1,1,
%U A110570 11,7,6,6,7,7,6,6,7,11,1,1,12,6,4,3,6,2,6,3,4,6,12,1,1,13,8,7,7,6,8,8,6,7,7
%N A110570 Triangle read by rows: T(n,0) = T(n,n) = 1 and for 0<k<n: T(n,k) = if k<=n/2 then T(n-k,0)+T(n-k,k) else T(k,n-k)+T(k,n).
%C A110570 T(n,k) = T(n,n-k);
%C A110570 row sums give A110571;
%C A110570 T(n,2) = A030451(n) for n>1;
%C A110570 T(n,k)=(1-0^A004197(n,k))*T(n-A004197(n,k),A004197(n,k))+1.
%H A110570 G. C. Greubel, <a href="/A110570/b110570.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%H A110570 <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>
%F A110570 T(n, k) = if s=0 then 1 else T(n-s, s)+1, where s=Min{k, n-k}.
%e A110570 . . . . . . . . . . 1 . . . . . . . . . . . .
%e A110570 . . . . . . . . . 1 . 1 . . . . . . . . . . .
%e A110570 . . . . . . . . 1 . x . 1 . . . . B = 1 + A .
%e A110570 . . . . . . . 1 . x . x . 1 . . . . . . . . .
%e A110570 . . . . . . 1 . x . x . x . 1 . . F = E + 1 .
%e A110570 . . . . . 1 . x . E . - . - . 1 . . . . . . .
%e A110570 . . . . 1 . x . x . \ . x . / . 1 . . . . . .
%e A110570 . . . 1 . x . x . x . \ . / . x . 1 . . . . .
%e A110570 . . 1 . - . A . x . x . F . x . x . 1 . . . .
%e A110570 . 1 . \ . / . x . x . x . x . x . x . 1 . . .
%e A110570 1 . x . B . x . x . x . x . x . x . x . 1 . .
%t A110570 T[n_, k_] := T[n, k] = If[Min[k, n - k] == 0, 1, 1 + T[n - Min[k, n - k], Min[k, n - k]]]; Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* _G. C. Greubel_, Aug 31 2017 *)
%Y A110570 Cf. A008949, A007318.
%K A110570 nonn,tabl
%O A110570 1,5
%A A110570 _Reinhard Zumkeller_, Jul 28 2005