The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A340025 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A340025

Number of connected graphs with vertices labeled with positive integers summing to n.
(history; published version)

#8 by Alois P. Heinz at Sun Jan 10 12:42:14 EST 2021

STATUS

proposed

approved

#7 by Andrew Howroyd at Sun Jan 10 12:32:07 EST 2021

STATUS

editing

proposed

#6 by Andrew Howroyd at Sun Jan 10 12:19:44 EST 2021

LINKS

Andrew Howroyd, <a href="/A340025/b340025.txt">Table of n, a(n) for n = 0..50</a>

STATUS

approved

editing

#5 by Susanna Cuyler at Sat Jan 02 18:03:37 EST 2021

STATUS

proposed

approved

#4 by Andrew Howroyd at Sat Jan 02 13:05:43 EST 2021

STATUS

editing

proposed

#3 by Andrew Howroyd at Sat Jan 02 13:04:12 EST 2021

PROG

(PARI) \\ See A340022 for permcount, edges.

permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}

edges(v) = {sum(i=2, #v, sum(j=1, i-1, gcd(v[i], v[j]))) + sum(i=1, #v, v[i]\2)}

CROSSREFS

Cf. A001349, A337717, A340022, A340026, A340027.

#2 by Andrew Howroyd at Fri Jan 01 21:51:12 EST 2021

NAME

allocated for Andrew HowroydNumber of connected graphs with vertices labeled with positive integers summing to n.

DATA

1, 1, 2, 4, 12, 41, 210, 1478, 17128, 352926, 14181309, 1129005180, 175491164826, 52346463432414, 29666505555854777, 31806668884174645842, 64442744342933382243031, 246898165053174167804654086, 1791518193851453375966274280997, 24668222649527263942329934357240780

OFFSET

0,3

PROG

(PARI)

InvEulerT(v)={my(p=log(1+x*Ser(v))); dirdiv(vector(#v, n, polcoef(p, n)), vector(#v, n, 1/n))}

permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}

edges(v) = {sum(i=2, #v, sum(j=1, i-1, gcd(v[i], v[j]))) + sum(i=1, #v, v[i]\2)}

seq(n) = {concat([1], InvEulerT(Vec(sum(k=1, n, my(s=0); forpart(p=k, s+=permcount(p) * 2^edges(p) * x^k/prod(j=1, #p, 1 - x^p[j] + O(x^(n-k+1)))); s/k!))))}

CROSSREFS

Cf. A001349, A337717, A340022.

KEYWORD

allocated

nonn

AUTHOR

Andrew Howroyd, Jan 01 2021

STATUS

approved

editing

#1 by Andrew Howroyd at Sat Dec 26 17:58:29 EST 2020

NAME

allocated for Andrew Howroyd

KEYWORD

allocated

STATUS

approved