OFFSET
1,2
COMMENTS
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).
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
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
EXAMPLE
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;
...
MAPLE
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, May 04 2008
MATHEMATICA
nn = 10; Map[Select[#, # > 0 &] &, Drop[CoefficientList[
Series[y x/(1 - x - y x + y x^3)/(1 - x), {x, 0, nn}], {x, y}],
1]] // Grid (* Geoffrey Critzer, Mar 17 2015 *)
PROG
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Mar 20 2005
EXTENSIONS
Edited by M. F. Hasler, Apr 26 2008
More terms from R. J. Mathar and Alec Mihailovs (alec(AT)mihailovs.com), May 04 2008
STATUS
approved