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A329052 Array read by antidiagonals: T(n,m) is the number of unlabeled bicolored acyclic graphs with n nodes of one color and m of the other. 2
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 5, 10, 10, 5, 1, 1, 6, 15, 21, 15, 6, 1, 1, 7, 21, 38, 38, 21, 7, 1, 1, 8, 28, 62, 82, 62, 28, 8, 1, 1, 9, 36, 95, 158, 158, 95, 36, 9, 1, 1, 10, 45, 138, 278, 356, 278, 138, 45, 10, 1, 1, 11, 55, 192, 459, 724, 724, 459, 192, 55, 11, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The two color classes are not interchangeable. Adjacent nodes cannot have the same color.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..1325

EXAMPLE

Array begins:

=======================================================

n\m | 0  1   2    3    4     5     6      7      8

----+--------------------------------------------------

  0 | 1, 1,  1,   1,   1,    1,    1,     1,     1, ...

  1 | 1, 2,  3,   4,   5,    6,    7,     8,     9, ...

  2 | 1, 3,  6,  10,  15,   21,   28,    36,    45, ...

  3 | 1, 4, 10,  21,  38,   62,   95,   138,   192, ...

  4 | 1, 5, 15,  38,  82,  158,  278,   459,   716, ...

  5 | 1, 6, 21,  62, 158,  356,  724,  1359,  2388, ...

  6 | 1, 7, 28,  95, 278,  724, 1690,  3612,  7143, ...

  7 | 1, 8, 36, 138, 459, 1359, 3612,  8731, 19404, ...

  8 | 1, 9, 45, 192, 716, 2388, 7143, 19404, 48213, ...

  ...

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(EulerXY(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 A329055.

Antidiagonal sums are A329053.

The equivalent array for labeled nodes is A328887.

Cf. A329054.

Sequence in context: A108086 A130595 A108363 * A076831 A197061 A230861

Adjacent sequences:  A329049 A329050 A329051 * A329053 A329054 A329055

KEYWORD

nonn,tabl,changed

AUTHOR

Andrew Howroyd, Nov 02 2019

STATUS

approved

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Last modified January 21 21:30 EST 2020. Contains 331128 sequences. (Running on oeis4.)