|
| |
|
|
A132089
|
|
Triangle T, read by rows, equal to the matrix square of Losanitsch's triangle (A034851).
|
|
0
|
|
|
|
1, 2, 1, 3, 2, 1, 6, 6, 4, 1, 10, 12, 12, 4, 1, 20, 30, 36, 18, 6, 1, 36, 62, 92, 56, 27, 6, 1, 72, 144, 246, 188, 110, 36, 8, 1, 136, 304, 600, 536, 380, 152, 48, 8, 1, 272, 680, 1504, 1576, 1296, 644, 248, 60, 10, 1, 528, 1448, 3576, 4256, 4008, 2332, 1080, 320, 75, 10
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
Conjectures: (1) The first column equals the row sums of Losanitsch's triangle (which equals A005418). (2) Let L^n denote the n-th power of Losanitsch's triangle. Then the first column of L^(n+1) equals the row sums of L^n.
|
|
|
LINKS
|
|
|
|
PROG
|
(PARI) s=13; L=matrix(s, s); T(n, k)= (1/2) *(binomial(n, k)+binomial(n%2, k%2)*binomial(n\2, k\2)); for(n=1, s, for(k=1, s, L[n, k]=T(n-1, k-1))); L2=L*L; for(n=1, s, for(k=1, n, print1(L2[n, k], ", ")));
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
