A127057 Triangle T(n,k), partial row sums of the n-th row of A127013 read right to left.

1, 3, 1, 4, 1, 1, 7, 3, 1, 1, 6, 1, 1, 1, 1, 12, 6, 3, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 15, 7, 3, 3, 1, 1, 1, 1, 13, 4, 4, 1, 1, 1, 1, 1, 1, 18, 8, 3, 3, 3, 1, 1, 1, 1, 1, 12, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 28, 16, 10, 6, 3, 3, 1, 1, 1, 1, 1, 1, 14, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 24, 10, 3, 3, 3, 3, 3, 1, 1

Offset

1,2

Comments

Also partial row sums of the n-th row of A126988 read left to right. - Reinhard Zumkeller, Jan 21 2014

Links

Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

Formula

T(n,k) = Sum_{i=1..n-k+1} A127013(n,i), n>=1, 1<=k<=n.

T(n,k) = Sum_{i=k..n} A126988(n,i).

Row sums: Sum_{k=1..n} T(n,k) = A038040(n).

T(n,1) = A000203(n).

T = A126988 * M as infinite lower triangular matrices, M = (1; 1, 1; 1, 1, 1; ...).

Example

The triangle starts
   1;
   3, 1;
   4, 1, 1;
   7, 3, 1, 1;
   6, 1, 1, 1, 1;
  12, 6, 3, 1, 1, 1;
   8, 1, 1, 1, 1, 1, 1;
  15, 7, 3, 3, 1, 1, 1, 1;
  13, 4, 4, 1, 1, 1, 1, 1, 1;
  18, 8, 3, 3, 3, 1, 1, 1, 1, 1; ...

Mathematica

A126988[n_, m_]:= If[Mod[n, m]==0, n/m, 0];
T[n_, m_]:= Sum[A126988[n, j], {j, m, n}];
Table[T[n, m], {n, 1, 12}, {m, 1, n}]//Flatten (* G. C. Greubel, Jun 03 2019 *)

Prog

(Haskell)
a127057 n k = a127057_tabl !! (n-1) !! (k-1)
a127057_row n = a127057_tabl !! (n-1)
a127057_tabl = map (scanr1 (+)) a126988_tabl
-- Reinhard Zumkeller, Jan 21 2014
(PARI)
A126988(n, k) = if(n%k==0, n/k, 0);
T(n, k) = sum(j=k, n, A126988(n, j));
for(n=1, 12, for(k=1, n, print1(T(n, k), ", "))) \\ G. C. Greubel, Jun 03 2019
(Magma)
A126988:= func< n, k | (n mod k) eq 0 select n/k else 0 >;
T:= func< n, k | (&+[A126988(n, j): j in [k..n]]) >;
[[T(n, k): k in [1..n]]: n in [1..12]]; // G. C. Greubel, Jun 03 2019
(Sage)
def A126988(n, k):
    if (n%k==0): return n/k
    else: return 0
def T(n, k): return sum(A126988(n, j) for j in (k..n))
[[T(n, k) for k in (1..n)] for n in (1..12)] # G. C. Greubel, Jun 03 2019

Crossrefs

Cf. A126988, A127013, A000203, A038040.

Sequence in context: A130307 A130314 A334466 * A143355 A143319 A078011

Adjacent sequences: A127054 A127055 A127056 * A127058 A127059 A127060

Keyword

nonn,tabl

Author

Gary W. Adamson, Jan 04 2007

Extensions

Edited and extended by R. J. Mathar, Jul 23 2008

Status

approved