|
Search: id:A073253
|
|
|
| A073253 |
|
Table of expansion of Product (1+(xy)^n/y)(1+(xy)^n/x), n>0 by antidiagonals. |
|
+0
1
|
|
| 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 0, 2, 2, 0, 0, 0, 0, 1, 3, 1, 0, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 2, 5, 2, 0, 0, 0, 0, 0, 0, 1, 5, 5, 1, 0, 0, 0, 0, 0, 0, 0, 3, 7, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1, 7, 7, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 11, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 11, 11, 2, 0
(list; table; graph; listen)
|
|
|
OFFSET
|
0,13
|
|
|
COMMENT
|
Combinatorial interpretation is number of partitions of Gaussian integer n+ki into distinct parts of form a+(a-1)i and (b-1)+bi, a,b>0.
Jacobi triple product identity implies the g.f. equals the Ramanujan theta function divided by Product (1-(xy)^m), m>0.
|
|
REFERENCES
|
J. H. van Lint and R. M. Wilson, A Course in Combinatorics, Cambridge Univ. Press, 1992. p. 141.
|
|
LINKS
|
Index entries for Gaussian integers and primes
|
|
EXAMPLE
|
1; 1,1; 0,1,0; 0,1,1,0; 0,1,2,1,0; 0,0,2,2,0,0; 0,0,1,3,1,0,0; ...
|
|
PROGRAM
|
(PARI) T(n, k)=if(n<0|k<0, 0, polcoeff(polcoeff(prod(i=1, max(n, k), (1+x^i*y^(i-1))*(1+x^(i-1)*y^i), 1+x*O(x^n)+y*O(y^k)), n), k))
|
|
CROSSREFS
|
A073252 gives antidiagonal sums.
Sequence in context: A051127 A070176 A092606 this_sequence A004198 A116402 A093323
Adjacent sequences: A073250 A073251 A073252 this_sequence A073254 A073255 A073256
|
|
KEYWORD
|
nonn,tabl,easy
|
|
AUTHOR
|
Michael Somos, Jul 23, 2002
|
|
|
Search completed in 0.002 seconds
|
