cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A123937 Triangle read by rows: T(x, y) = 0 if y > x, = 1 if y = 0, or = 2*Sum_{k >= 1, x-k^2 >= y} T(x-k^2, y-1) otherwise. The zeros are omitted from the sequence.

Original entry on oeis.org

1, 1, 2, 1, 2, 4, 1, 2, 4, 8, 1, 4, 4, 8, 16, 1, 4, 12, 8, 16, 32, 1, 4, 12, 32, 16, 32, 64, 1, 4, 12, 32, 80, 32, 64, 128, 1, 4, 16, 32, 80, 192, 64, 128, 256, 1, 6, 16, 56, 80, 192, 448, 128, 256, 512, 1, 6, 24, 56, 176, 192, 448, 1024, 256, 512, 1024
Offset: 0

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Author

David W. Wilson, Oct 30 2006

Keywords

Comments

Comments from R. J. Mathar, Oct 31 2006:
This sequence provides the seeds for the construction of columns (vertical recurrence) of A122510 insofar as each row of A123937 provides two sides of auxiliary arrays b(.,.,.) from which a column of A122510 emerges as the third side:
A122510(d,n)=b(0,d,n) [with an auxiliary, virtual A122510(0,n)=1].
Seeds to construct two sides of b(.,.,.):
b(x,0,n)=A123937(n,x) for x<=n; b(n,y,n)=A123937(n,n) for y>=0.
Recurrence within the b(.,.,.) : b(x,y,n)=b(x,y-1,n)+b(x+1,y-1,n) for x
Graphical support as if the array were built top-down and left-to-right from the seeds:
Triangle stump ("stump" means cut-off/finiteness at the bottom and top)
...................b(n,0,n)...b(n,1,n)...b(n,2,n)....
..............................
.............b(2,0,n)...b(2,1,n)....
.........b(1,0,n)...b(1,1,n)....
...b(0,0,n)..b(0,1,n)...b(0,2,n)....
equals triangle stump (note that the top line is constant) T(x,y)=A123937(x,y)
...................T(n,n)...T(n,n)...T(n,n)....
..............................
.............T(n,2).....b(2,1,n)....
.........T(n,1).....b(1,1,n)....
...T(n,0)....b(0,1,n)...b(0,2,n)....
equals triangle stump
...................T(n,n)...T(n,n)...T(n,n)....
..............................
.............T(n,2).....b(2,1,n)....
.........T(n,1).....b(1,1,n)....
...T(n,0)...A122510(1,n).A122510(2,n).A122510(3,n)....

Examples

			Triangle begins:
1
1 2
1 2 4
1 2 4 8
1 4 4 8 16
1 4 12 8 16 32
1 4 12 32 16 32 64
1 4 12 32 80 32 64 128

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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