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A329054
Array read by antidiagonals: T(n,m) is the number of unlabeled bicolored trees with n nodes of one color and m of the other.
6
1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 4, 2, 1, 0, 0, 1, 3, 7, 7, 3, 1, 0, 0, 1, 3, 10, 14, 10, 3, 1, 0, 0, 1, 4, 14, 28, 28, 14, 4, 1, 0, 0, 1, 4, 19, 45, 65, 45, 19, 4, 1, 0, 0, 1, 5, 24, 73, 132, 132, 73, 24, 5, 1, 0
OFFSET
0,18
COMMENTS
The two color classes are not interchangeable. Adjacent nodes cannot have the same color.
Essentially the same data as given in the irregular triangle A122085, but including complete columns for n = 0 and m = 0 to give a regular array.
LINKS
EXAMPLE
Array begins:
===================================================
n\m | 0 1 2 3 4 5 6 7 8
----+----------------------------------------------
0 | 1, 1, 0, 0, 0, 0, 0, 0, 0, ...
1 | 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
2 | 0, 1, 1, 2, 2, 3, 3, 4, 4, ...
3 | 0, 1, 2, 4, 7, 10, 14, 19, 24, ...
4 | 0, 1, 2, 7, 14, 28, 45, 73, 105, ...
5 | 0, 1, 3, 10, 28, 65, 132, 242, 412, ...
6 | 0, 1, 3, 14, 45, 132, 316, 693, 1349, ...
7 | 0, 1, 4, 19, 73, 242, 693, 1742, 3927, ...
8 | 0, 1, 4, 24, 105, 412, 1349, 3927, 10079, ...
...
PROG
(PARI)
EulerXY(A)={my(j=serprec(A, x)); exp(sum(i=1, j, 1/i * subst(subst(A + x * O(x^(j\i)), x, x^i), y, y^i)))}
R(n)={my(A=O(x)); for(j=1, 2*n, A = if(j%2, 1, y)*x*EulerXY(A)); A};
P(n)={my(r1=R(n), r2=x*EulerXY(r1), s=r1+r2-r1*r2); Vec(1 + s)}
{ my(A=P(10)); for(n=0, #A\2, for(k=0, #A\2, print1(polcoef(A[n+k+1], k), ", ")); print) }
CROSSREFS
Main diagonal is A119857.
Antidiagonal sums are A122086.
The equivalent array for labeled nodes is A072590.
Sequence in context: A368122 A281459 A163528 * A239509 A360985 A335833
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Nov 02 2019
STATUS
approved