The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A007717 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A007717

Number of symmetric polynomial functions of degree n of a symmetric matrix (of indefinitely large size) under joint row and column permutations. Also number of multigraphs with n edges (allowing loops) on an infinite set of nodes.
(history; published version)

#62 by Michael De Vlieger at Mon Jan 08 20:59:25 EST 2024

STATUS

proposed

approved

#61 by Andrew Howroyd at Mon Jan 08 20:25:19 EST 2024

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editing

proposed

#60 by Gus Wiseman at Mon Jan 08 20:17:13 EST 2024

EXAMPLE

(End)

From Gus Wiseman, Jan 08 2024: (Start)

Non-isomorphic representatives of the a(1) = 1 through a(3) = 7 rooted loopless multigraphs (root shown as singleton):

{{1}} {{1},{1,2}} {{1},{1,2},{1,2}}

{{1},{2,3}} {{1},{1,2},{1,3}}

{{1},{1,2},{2,3}}

{{1},{1,2},{3,4}}

{{1},{2,3},{2,3}}

{{1},{2,3},{2,4}}

{{1},{2,3},{4,5}}

Discussion

Mon Jan 08

20:25

Andrew Howroyd: Thanks a lot for the example.

#59 by Andrew Howroyd at Mon Jan 08 12:26:41 EST 2024

COMMENTS

a(n) is the number of unlabeled loopless multigraphs with n edges rooted at one vertex. - Andrew Howroyd, Nov 22 2020

STATUS

approved

editing

#58 by N. J. A. Sloane at Sun Nov 22 20:23:29 EST 2020

STATUS

proposed

approved

#57 by Andrew Howroyd at Sun Nov 22 13:24:15 EST 2020

STATUS

editing

proposed

#56 by Andrew Howroyd at Sun Nov 22 12:13:30 EST 2020

COMMENTS

a(n) is the number of unlabeled multigraphs with n edges rooted at one vertex. - Andrew Howroyd, Nov 22 2020

PROG

(PARI) \\ See A339065 for G.

seq(n)={my(A=O(x*x^n)); Vec(G(2*n, x+A, [1]))} \\ Andrew Howroyd, Nov 22 2020

CROSSREFS

Cf. A000664, A002620, A007716, A007719, A020555, A050531, A050532, A050535, A052171, A053418, A053419, A094574, A316972, A316974, A318951, A339065.

STATUS

approved

editing

#55 by Alois P. Heinz at Sun Feb 09 12:06:45 EST 2020

STATUS

proposed

approved

#54 by Andrew Howroyd at Sun Feb 09 12:05:19 EST 2020

STATUS

editing

proposed

#53 by Andrew Howroyd at Sun Feb 09 11:15:17 EST 2020

CROSSREFS

Row n=2 of A331485.

STATUS

approved

editing