A137682 Left border of triangle A137680.

1, 1, 3, 7, 17, 40, 96, 228, 544, 1296, 3089, 7361, 17544, 41810, 99643, 237471, 565946, 1348773, 3214424, 7660679, 18257085, 43510652, 103695461, 247129108, 588963062, 1403628615, 3345155947, 7972242937, 18999609718, 45280252031

Offset: 1

Author

Gary W. Adamson, Feb 05 2008

Keywords

• nonn

Comments

Each term in the sequence (n > 1) = sum of previous terms of triangle A137680 = partial sums of sequence A137681: (1, 2, 4, 10, 23, ...).

Starting (1, 3, 7, ...) = INVERT transform of A160096. - Gary W. Adamson, May 01 2009

Examples

			First few rows of triangle A137680 =
  1;
  1, 1;
  3, 0, 1;
  7, 2, 0, 1;
  ...
a(5) = 17 is the sum of 1 through 4 row terms of triangle A137680: (1 + 2 + 4 + 10); where (1, 2, 4, 10, 23, ...) = A137681 = row sums of triangle A137680 = first difference row of A137682, n > 1.
		

Crossrefs

Cf. A137680, A137681.

Cf. A160096.

Programs

Maple

A137682 := proc(n)
    A137680(n,1) ;
end proc:
seq(A137682(n),n=1..30) ; # R. J. Mathar, Aug 12 2012

Mathematica

T[n_, k_] := T[n, k] = Which[k < 1 || k > n, 0, n == 1, 1, k == 1, Sum[T[r, j], {r, 1, n-1}, {j, 1, r}], True, T[n-1, k-1] - T[n-k, k-1]];
a[n_] := T[n, 1];
Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Sep 19 2024, after R. J. Mathar in A137680 *)

Formula

Partial sums of sequence A137681 prefaced with a 1. a(n) is the sum of all terms in rows 1 through (n-1) in triangle A137680.