The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A297029 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A297029

Number of edge covers in the n-cocktail party graph.
(history; published version)

#12 by Charles R Greathouse IV at Sun Feb 16 08:33:52 EST 2025

LINKS

Eric Weisstein's World of Mathematics, <a href="httphttps://mathworld.wolfram.com/CocktailPartyGraph.html">Cocktail Party Graph</a>

Eric Weisstein's World of Mathematics, <a href="httphttps://mathworld.wolfram.com/EdgeCover.html">Edge Cover</a>

Discussion

Sun Feb 16

08:33

OEIS Server: https://oeis.org/edit/global/3014

#11 by N. J. A. Sloane at Wed Dec 27 10:44:10 EST 2017

STATUS

reviewed

approved

#10 by Robert G. Wilson v at Wed Dec 27 10:32:38 EST 2017

STATUS

proposed

reviewed

#9 by Jean-François Alcover at Wed Dec 27 10:19:18 EST 2017

STATUS

editing

proposed

#8 by Jean-François Alcover at Wed Dec 27 10:19:13 EST 2017

MATHEMATICA

a[n_] := Sum[(-1)^(i + j)*Binomial[n, i]*Binomial[2*(n - i), j] * 2^(Binomial[2*n - j, 2] - i), {i, 0, n}, {j, 0, 2*(n - i)}];

Array[a, 10] (* Jean-François Alcover, Dec 27 2017, after Andrew Howroyd *)

STATUS

approved

editing

#7 by Joerg Arndt at Wed Dec 27 03:11:15 EST 2017

STATUS

proposed

approved

#6 by Andrew Howroyd at Wed Dec 27 02:11:22 EST 2017

STATUS

editing

proposed

#5 by Andrew Howroyd at Wed Dec 27 00:24:25 EST 2017

DATA

0, 7, 2902, 14872877, 1057937802444, 1139547636041211251, 19276901022645375031039586, 5187230738913145148610293591969497, 22294621657566842766129181417308087584893464, 1532378628985463601567919431617165851656712130496565087

LINKS

Andrew Howroyd, <a href="/A297029/b297029.txt">Table of n, a(n) for n = 1..25</a>

FORMULA

a(n) = Sum_{i=0..n} Sum_{j=0, 2*(n-i)} (-1)^(i+j)*binomial(n, i)*binomial(2*(n-i), j)*2^(binomial(2*n-j, 2)-i). - Andrew Howroyd, Dec 27 2017

PROG

(PARI) a(n)={sum(i=0, n, sum(j=0, 2*(n-i), (-1)^(i+j)*binomial(n, i)*binomial(2*(n-i), j)*2^(binomial(2*n-j, 2)-i)))} \\ Andrew Howroyd, Dec 27 2017

KEYWORD

nonn,more,new

EXTENSIONS

Terms a(5) and beyond from Andrew Howroyd, Dec 27 2017

STATUS

approved

editing

#4 by N. J. A. Sloane at Mon Dec 25 11:28:02 EST 2017

STATUS

proposed

approved

#3 by Eric W. Weisstein at Sun Dec 24 09:16:39 EST 2017

STATUS

editing

proposed