|
Search: id:A003293
|
|
|
| A003293 |
|
Number of planar partitions of n decreasing across rows.
(Formerly M1058)
|
|
+0
2
|
|
| 1, 1, 2, 4, 7, 12, 21, 34, 56, 90, 143, 223, 348, 532, 811, 1224, 1834, 2725, 4031, 5914, 8638, 12540, 18116, 26035, 37262, 53070, 75292, 106377, 149738, 209980, 293473, 408734, 567484, 785409, 1083817, 1491247, 2046233, 2800125, 3821959, 5203515
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
Also number of planar partitions monotonically decreasing down anti-diagonals (i.e., with b(n,k)<=b(n-1,k+1)). Transpose (to get planar partitions decreasing down columns), then take the conjugate of each row. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), May 15 2006
|
|
REFERENCES
|
D. M. Bressoud, Proofs and Confirmations, Camb. Univ. Press, 1999; p. 133.
M. S. Cheema and W. E. Conway, Numerical investigation of certain asymptotic results in the theory of partitions, Math. Comp., 26 (1972), 999-1005.
|
|
FORMULA
|
G.f.: Product (1 - x^k )^{-c(k)}, c(k) = 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, ....
Euler transform of A110654. - Michael Somos Sep 19 2006
|
|
PROGRAM
|
(PARI) {a(n)=if(n<0, 0, polcoeff( prod(k=1, n, (1-x^k+x*O(x^n))^-ceil(k/2)), n))} /* Michael Somos Sep 19 2006 */
|
|
CROSSREFS
|
Sequence in context: A079970 A079816 A100482 this_sequence A094974 A100671 A005251
Adjacent sequences: A003290 A003291 A003292 this_sequence A003294 A003295 A003296
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
njas
|
|
EXTENSIONS
|
More terms from James A. Sellers (sellersj(AT)math.psu.edu), Feb 06 2000. Additional comments from Michael Somos, May 19, 2000.
|
|
|
Search completed in 0.002 seconds
|
