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Revision History for A000368

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A000368

Number of connected graphs with one cycle of length 4.
(history; published version)

#79 by Michael De Vlieger at Sun Jul 28 16:49:54 EDT 2024

STATUS

reviewed

approved

#78 by Andrew Howroyd at Sun Jul 28 16:42:26 EDT 2024

STATUS

proposed

reviewed

#77 by Jason Yuen at Sun Jul 28 15:59:22 EDT 2024

STATUS

editing

proposed

#76 by Jason Yuen at Sun Jul 28 15:57:52 EDT 2024

FORMULA

| (f(D[1])^4 + 2*f(D[1])^3 + 3*f(D[1])^2 + 2 * f(D[1]))/8, if d = 1,

| ((3*f(D[2])^2+f(D[2]]))*f(D[1])^2+(f(D[2])^2+3*f(D[2]]))*f(D[1]]))/4,

STATUS

approved

editing

Discussion

Sun Jul 28

15:59

Jason Yuen: I used the PARI program to fix these brackets.

#75 by OEIS Server at Sat Dec 26 08:46:24 EST 2020

LINKS

Vaclav Kotesovec, <a href="/A000368/b000368_1.txt">Table of n, a(n) for n = 4..2000</a> (terms 4..43 from Sean A. Irvine, 44..200 from Washington Bomfim)

#74 by Vaclav Kotesovec at Sat Dec 26 08:46:24 EST 2020

STATUS

proposed

approved

Discussion

Sat Dec 26

08:46

OEIS Server: Installed new b-file as b000368.txt.  Old b-file is now b000368_1.txt.

#73 by Washington Bomfim at Sat Dec 26 08:21:21 EST 2020

STATUS

editing

proposed

#72 by Washington Bomfim at Sat Dec 26 08:20:28 EST 2020

PROG

(PARI) g(Q)={my(V=Vec(Q), D=Set(V), d=#D); if(d==4, return(3*f[D[1]]*f[D[2]]*f[D[3]]*f[D[4]]));

g(Q) = {my(V=Vec(Q), D=Set(V), d=#D); if(d==4, return(3*f[D[1]]*f[D[2]]*f[D[3]] *f[D[4]])); if(d==1, return((f[D[1]]^4+2*f[D[1]]^3+3*f[D[1]]^2+2*f[D[1]])/8));

my(k=1, m = #select(x->x == D[k], V), t); while(m==1, k++; m = #select(x->x == D[k], V)); t = D[1]; D[1] = D[k]; D[k] = t;

seq(max_n) = { my(s, a = vector(max_n), U); f = vector(max_n); f[1] = 1;

for(j=1, max_n - 1, if(j%100==0, print(j)); f[j+1] = 1/j * sum(k=1, j, sumdiv(k, d, d * f[d]) * f[j-k+1]));

for(n=4, max_n, s=0; forpart(Q = n, s += gif( (Q), [1, n], [4, 4]); a > Q[n3] = s); a && (Q[3]-1 > Q[4..max_n2] }; \\ _Washington Bomfim_, Jul 19 2012 and Dec 22 2020),

U = U / (f[Q[4] + 1] * f[Q[3] - 1]) * f[Q[4]] * f[Q[3]], U = g(Q)); s += U,

[1, n], [4, 4]); a[n] = s; if(n % 100 == 0, print(n": " s))); a[4..max_n] };

\\ Washington Bomfim, Jul 19 2012 and Dec 22 2020

STATUS

reviewed

editing

#71 by Vaclav Kotesovec at Sat Dec 26 02:58:44 EST 2020

STATUS

proposed

reviewed

Discussion

Sat Dec 26

08:14

Washington Bomfim: Sorry, no lines longer than 80 characters next time.   
To compute 10,000 terms is not practical with my program. I'm now at n = 1600. Probably it will run all day to reach n=2,000.

#70 by Washington Bomfim at Fri Dec 25 18:45:40 EST 2020

STATUS

editing

proposed

Discussion

Fri Dec 25