The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A053419 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A053419

Number of graphs with loops (symmetric relations) with n edges.
(history; published version)

#23 by Alois P. Heinz at Thu Dec 03 07:49:50 EST 2020

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proposed

approved

#22 by Michel Marcus at Thu Dec 03 02:59:05 EST 2020

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editing

proposed

#21 by Michel Marcus at Thu Dec 03 02:58:59 EST 2020

MATHEMATICA

seq[n_] := Module[{A = O[x]^n}, G[2n, x+A, {1}] // CoefficientList[#, x]&]; (* _Jean-François Alcover_, Dec 03 2020, using _Andrew Howroyd_'s code for g.f. G in A339063 *)

(* Jean-François Alcover, Dec 03 2020, using Andrew Howroyd's code for g.f. G in A339063 *)

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proposed

editing

#20 by Jean-François Alcover at Thu Dec 03 01:25:01 EST 2020

STATUS

editing

proposed

#19 by Jean-François Alcover at Thu Dec 03 01:24:54 EST 2020

MATHEMATICA

seq[n_] := Module[{A = O[x]^n}, G[2n, x+A, {1}] // CoefficientList[#, x]&];

(* Jean-François Alcover, Dec 03 2020, using Andrew Howroyd's code for g.f. G in A339063 *)

STATUS

approved

editing

#18 by N. J. A. Sloane at Sun Nov 22 20:23:42 EST 2020

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proposed

approved

#17 by Andrew Howroyd at Sun Nov 22 13:24:29 EST 2020

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editing

proposed

#16 by Andrew Howroyd at Sun Nov 22 12:09:05 EST 2020

COMMENTS

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

PROG

(PARI) \\ See A339063 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, A000666, A007716, A007717, A020555, A050535, A053419, A094574, A191970 (multisets), A316974, A339063.

STATUS

approved

editing

#15 by R. J. Mathar at Mon Aug 03 05:31:33 EDT 2020

STATUS

editing

approved

#14 by R. J. Mathar at Mon Aug 03 05:31:29 EDT 2020

CROSSREFS

Cf. A000664, A000666, A007716, A007717, A020555, A050535, A053419, A094574, A191970, (multisets), A316974.

STATUS

approved

editing