The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A261919 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A261919

Number of n-node unlabeled graphs without isolated nodes or endpoints (i.e., no nodes of degree 0 or 1).
(history; published version)

#35 by Bruno Berselli at Thu Sep 12 04:43:20 EDT 2019

STATUS

proposed

approved

#34 by Jean-François Alcover at Thu Sep 12 03:23:13 EDT 2019

STATUS

editing

proposed

#33 by Jean-François Alcover at Thu Sep 12 03:23:06 EDT 2019

MATHEMATICA

permcount[v_] := Module[{m = 1, s = 0, k = 0, t}, For[i = 1, i <= Length[v], i++, t = v[[i]]; k = If[i > 1 && t == v[[i - 1]], k + 1, 1]; m *= t*k; s += t]; s!/m];

edges[v_] := Sum[GCD[v[[i]], v[[j]]], {i, 2, Length[v]}, {j, 1, i - 1}] + Total[Quotient[v, 2]];

b[n_] := Sum[permcount[p]*2^edges[p]*Coefficient[Product[1-x^p[[i]], {i, 1, Length[p]}], x, n-k]/k!, {k, 1, n}, {p, IntegerPartitions[k]}]; b[0] = 1;

a[n_] := b[n] - b[n-1];

a /@ Range[0, 19] (* Jean-François Alcover, Sep 12 2019, after Andrew Howroyd in A004110 *)

STATUS

approved

editing

#32 by OEIS Server at Fri Aug 16 07:50:09 EDT 2019

LINKS

Andrew Howroyd, <a href="/A261919/b261919_2.txt">Table of n, a(n) for n = 0..50</a> (terms 1..26 from Max Alekseyev)

#31 by Susanna Cuyler at Fri Aug 16 07:50:09 EDT 2019

STATUS

reviewed

approved

Discussion

Fri Aug 16

07:50

OEIS Server: Installed new b-file as b261919.txt.  Old b-file is now b261919_2.txt.

#30 by Joerg Arndt at Fri Aug 16 07:31:26 EDT 2019

STATUS

proposed

reviewed

#29 by Gus Wiseman at Fri Aug 16 00:49:24 EDT 2019

STATUS

editing

proposed

#28 by Gus Wiseman at Thu Aug 15 07:51:19 EDT 2019

LINKS

Gus Wiseman, Andrew Howroyd, <a href="/A261919/b261919_2.txt">Table of n, a(n) for n = 0..50</a> (terms 1..26 from Max Alekseyev)

#27 by Gus Wiseman at Thu Aug 15 07:49:33 EDT 2019

LINKS

Andrew Howroyd, Gus Wiseman, <a href="/A261919/b261919_2.txt">Table of n, a(n) for n = 10..50</a> (terms 1..26 from Max Alekseyev)

EXTENSIONS

a(0) = 1 prepended by Gus Wiseman, Aug 15 2019

#26 by Gus Wiseman at Thu Aug 15 07:47:13 EDT 2019

DATA

1, 0, 0, 1, 3, 11, 62, 510, 7459, 197867, 9808968, 902893994, 153723380584, 48443158427276, 28363698856991892, 30996526139142442460, 63502034434187094606966, 244852545450108200518282934, 1783161611521019613186341526720, 24603891216946828886755056314074748

OFFSET

1,4

0,5

FORMULA

Euler transform of A004108, if we assume A004108(1) = 0. - Gus Wiseman, Aug 15 2019