cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-17 of 17 results.

A289986 Number of connected 2n-regular loopless multigraphs on 2n unlabeled nodes.

Original entry on oeis.org

1, 1, 3, 120, 543116, 635669057538, 112368754788708539549
Offset: 0

Views

Author

Natan Arie Consigli, Aug 19 2017

Keywords

Comments

Multigraphs are loopless.
There are no (2n+1)-regular multigraphs with (2n+1) number of points, for every nonnegative n.

Crossrefs

Programs

  • nauty
    for n in {1..4}; do geng -c -d1 $[2*$n] -q | multig -m$[2*$n] -r$[2*$n] -u; done

Formula

a(n) = A328682(2*n, 2*n). - Andrew Howroyd, Mar 18 2020

Extensions

a(5)-a(6) from Andrew Howroyd, Mar 18 2020

A324217 Number of connected 2n-regular loopless multigraphs on seven unlabeled nodes.

Original entry on oeis.org

0, 1, 50, 933, 12465, 119906, 864705, 4930446, 23280925, 94308983, 336704397, 1081565510, 3176476119, 8638660038, 21978039571, 52745266132, 120228555981, 261785061087, 547126506745, 1102086250237, 2147107495684
Offset: 0

Views

Author

Natan Arie Consigli, Apr 30 2019

Keywords

Comments

There are no (2n+1)-regular graphs satisfying the condition above.
Multigraphs are loopless.
Initial terms computed with 'nauty and Traces' (see the link).

Crossrefs

Row n=7 of A328682.
Cf. A324218.

Programs

  • nauty
    for ((n=0;n<30;n=n+2)); do geng -c -d1 7 -q | multig -r${n} -u; done

Extensions

a(10)-a(20) from Andrew Howroyd, Mar 17 2020

A325474 Number of connected n-regular loopless multigraphs on eight unlabeled nodes.

Original entry on oeis.org

0, 0, 1, 20, 204, 1689, 13303, 90614, 543116, 2842431, 13218770, 55233883, 210199115, 736166006, 2395665563, 7301022565, 20981692199, 57188601747, 148588072319, 369611918382, 883579452509, 2036672785494, 4539872512172, 9811474182969, 20605911433906, 42141179374995
Offset: 0

Views

Author

Natan Arie Consigli, Aug 09 2019

Keywords

Comments

Multigraphs are loopless.
Initial terms computed using 'Nauty and Traces' (see the link).

Crossrefs

Row n=8 of A328682.

Programs

  • nauty
    for ((n=0;n<11;n++)); do geng -c -d1 8 -q | multig -r${n} -u; done

Extensions

Terms a(13) and beyond from Andrew Howroyd, Mar 17 2020

A319897 Number of connected regular loopless multigraphs on n unlabeled nodes with degree up to n.

Original entry on oeis.org

1, 1, 2, 1, 6, 7, 195, 984, 648947, 35494648, 689162614688, 250087643676776, 116889497942206867366
Offset: 0

Views

Author

Natan Arie Consigli, Nov 28 2018

Keywords

Comments

Initial terms computed using 'Nauty and Traces'.

Crossrefs

Formula

a(n) = Sum_{k=0..n} A328682(n, k). - Andrew Howroyd, Mar 18 2020

Extensions

a(1), a(8) corrected and a(10)-a(12) added by Andrew Howroyd, Mar 18 2020

A324221 Number of connected 2n-regular loopless multigraphs with five nodes.

Original entry on oeis.org

0, 1, 6, 15, 36, 72, 139, 244, 414, 663, 1030, 1540, 2247, 3187, 4433, 6036, 8088, 10658, 13861, 17785, 22571, 28329, 35227, 43401, 53049, 64333, 77485, 92697, 110235, 130324, 153268, 179326, 208843, 242115, 279529, 321422, 368226, 420319, 478182, 542238, 613017
Offset: 0

Views

Author

Natan Arie Consigli, Feb 18 2019

Keywords

Comments

There are no (2n+1)-regular multigraphs satisfying the condition above.
Multigraphs are loopless.
Initial terms computed with 'Nauty and Traces'.

Crossrefs

Row n=5 of A328682.

Programs

  • nauty
    for ((n=0;n<76;n=n+2)); do geng -c -d1 5 -q | multig -m${n} -u; done

Formula

Conjectures from Colin Barker, Feb 18 2019: (Start)
G.f.: x*(1 + 3*x - x^2 + 4*x^3 - x^4 + 6*x^5 + 4*x^7 - x^8 - x^9 + x^10) / ((1 - x)^6*(1 + x)^2*(1 + x^2)*(1 + x + x^2)).
a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + a(n-4) - 2*a(n-5) + 4*a(n-6) - 2*a(n-7) + a(n-8) - a(n-9) - 2*a(n-10) + 3*a(n-11) - a(n-12) for n>11.
(End)
Equivalent conjecture: 1152*a(n) = 6*n^5 + 30*n^4 + 220*n^3 + 540*n^2 + 1143*n - 353 + 72*A056594(n) + 128*A049347(n) + 153*A181983(n+1). - R. J. Mathar, Mar 09 2019

Extensions

a(28)-a(30) from Andrew Howroyd, Mar 18 2020

A325476 Number of connected regular loopless multigraphs on n unlabeled nodes of degree less than n.

Original entry on oeis.org

1, 1, 1, 1, 3, 7, 75, 984, 105831, 35494648, 53493557150, 250087643676776, 4520743153498327817, 272584534800111470995411
Offset: 0

Views

Author

Natan Arie Consigli, May 02 2019

Keywords

Comments

Multigraphs are loopless.
Initial terms computed using nauty and traces.

Examples

			There is no such thing as a graph with nodes of negative degree, and the "nodeless" graph has, according to the definition in the name, zero nodes of degree less than 0. So a(0) = 1.
		

Crossrefs

Programs

  • nauty
    for ((n=2; n<9; n++)); do
    a=0
    for ((d=0; d<${n}; d++)); do
    s=$(geng -c -d1 ${n} -q | multig -r${d} -u 2>&1 | cut -d ' ' -f 7 | grep -v '^$')
    a=$((a+s))
    done
    echo ${a}
    done
    # Andrey Zabolotskiy, Sep 26 2019

Formula

a(n) = Sum_{k=0..n-1} A328682(n, k). - Andrew Howroyd, Mar 18 2020

Extensions

a(10)-a(13) from Andrew Howroyd, Mar 18 2020

A327604 Number of connected 2n-regular loopless multigraphs on nine unlabeled nodes.

Original entry on oeis.org

0, 1, 832, 252207, 35241608, 2351580473, 89216898630, 2194653376016, 38376657658125, 509484171323720, 5390386822995890, 47150458233195944, 350827631527584993, 2271025998493100911, 13023793690772493636
Offset: 0

Views

Author

Natan Arie Consigli, Sep 18 2019

Keywords

Comments

There are no (2n+1)-regular graphs satisfying the condition above.
Multigraphs are loopless.
Initial terms computed with 'Nauty and Traces' (see the link).

Crossrefs

Row n=9 of A328682.

Programs

  • nauty
    for ((n=0;n<12;n=n+2)); do geng -c -d1 9 -q | multig -r${n} -u; done

Extensions

a(6)-a(14) from Andrew Howroyd, Mar 18 2020
Previous Showing 11-17 of 17 results.