The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 2
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,3
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<n.
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)....
LINKS
EXAMPLE
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
CROSSREFS
Sequence in context: A059268 A300653 A256009 * A138882 A074634 A152036
KEYWORD
nonn,tabl
AUTHOR
David W. Wilson, Oct 30 2006
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 24 16:05 EDT 2024. Contains 372778 sequences. (Running on oeis4.)