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

1,3

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

Links

Table of n, a(n) for n=1..30.

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.

Example

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.

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 *)

Crossrefs

Cf. A137680, A137681.

Cf. A160096.

Sequence in context: A309538 A036885 A247300 * A190360 A167213 A249753

Adjacent sequences: A137679 A137680 A137681 * A137683 A137684 A137685

Keyword

nonn

Author

Gary W. Adamson, Feb 05 2008

Status

approved