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).

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, 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, 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

Offset

1,5

Comments

T(n,k) = T(n,n-k);

row sums give A110571;

T(n,2) = A030451(n) for n>1;

T(n,k)=(1-0^A004197(n,k))*T(n-A004197(n,k),A004197(n,k))+1.

Links

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Index entries for triangles and arrays related to Pascal's triangle

Formula

T(n, k) = if s=0 then 1 else T(n-s, s)+1, where s=Min{k, n-k}.

Example

. . . . . . . . . . 1 . . . . . . . . . . . .
. . . . . . . . . 1 . 1 . . . . . . . . . . .
. . . . . . . . 1 . x . 1 . . . . B = 1 + A .
. . . . . . . 1 . x . x . 1 . . . . . . . . .
. . . . . . 1 . x . x . x . 1 . . F = E + 1 .
. . . . . 1 . x . E . - . - . 1 . . . . . . .
. . . . 1 . x . x . \ . x . / . 1 . . . . . .
. . . 1 . x . x . x . \ . / . x . 1 . . . . .
. . 1 . - . A . x . x . F . x . x . 1 . . . .
. 1 . \ . / . x . x . x . x . x . x . 1 . . .
1 . x . B . x . x . x . x . x . x . x . 1 . .

Mathematica

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 *)

Crossrefs

Cf. A008949, A007318.

Sequence in context: A095140 A225043 A125605 * A341314 A335174 A082905

Adjacent sequences: A110567 A110568 A110569 * A110571 A110572 A110573

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Jul 28 2005

Status

approved