1,2

Original definition was "Triangle, row sums are A001924". Reading the rows of the triangle as antidiagonals of a square array allows a precise, yet simple definition and a method for computing the terms. - M. F. Hasler, Apr 26 2008

When formatted as a triangle, row sums are A001924: 1, 3, 7, 14, 26...(apply the partial sum operator twice to the Fibonacci sequence).

Alec Mihailovs (alec(AT)mihailovs.com), May 04 2008, Table of n, a(n) for n = 1..467

The triangle is extracted from A * B; where A = [1; 2, 1; 3, 2, 1;...], B = [1; 0, 1; 0, 1, 1; 0, 0, 2, 1;...]; both infinite lower triangular matrices with the rest of the terms zeros. The sequence in "B" (1, 0, 1, 0, 1, 1, 0, 0, 2, 1...) = A026729.

As a square array, g.f. Sum T[i,j] x^j y^i = xy/((1-(1+x)y)*(1-x)^2). - Alec Mihailovs (alec(AT)mihailovs.com), Apr 26 2008

The first few rows of the triangle (= rising diagonals of the square array) are:

1;

2, 1;

3, 3, 1;

4, 5, 4, 1;

5, 7, 8, 5, 1;

6, 9, 12, 12, 6, 1;

...

A104732 := proc(i, j) coeftayl(coeftayl(x*y/(1-x)^2/(1-y*(1+x)), y=0, i), x=0, j) ; end: for d from 1 to 20 do for j from d to 1 by -1 do printf("%d, ", A104732(d-j+1, j)) ; od: od: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 04 2008

Python program from Alec Mihailovs (alec(AT)mihailovs.com), May 04 2008. Replace leading dots by spaces.

def A104732_rows(n):

........"""Produces n rows of A104732 triangle"""

........from operator import iadd

........a, b, c = [], [1], [1]

........for i in range(2, n+1):

................a, b = b, [i]+map(iadd, a, b[:-1])+[1]

................c+=b

........return c

Cf. A001924, A026729.

Adjacent sequences: A104729 A104730 A104731 this_sequence A104733 A104734 A104735

Sequence in context: A115131 A117895 A128139 this_sequence A132108 A125175 A073020

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 20 2005

Edited by M. F. Hasler (www.univ-ag.fr/~mhasler), Apr 26 2008

More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Alec Mihailovs (alec(AT)mihailovs.com), May 04 2008