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.

Showing 1-8 of 8 results.

A101469 Erroneous version of A058832.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1260, 57120
Offset: 0

Views

Author

Keywords

Comments

These numbers should have been halved.

References

  • R. C. Read and N. C. Wormald, Number of labeled 4-regular graphs, J. Graph Theory, 4 (1980), 203-212.

A058831 Number of labeled n-node 4-valent graphs containing two nonadjacent double edges.

Original entry on oeis.org

0, 0, 0, 0, 3, 30, 405, 10080, 369180, 17959158, 1092909510, 81043601760, 7195434965235, 753877707936210, 92048844661576803, 12957249486666966390, 2083048648390795634640, 379312444955136162744540
Offset: 0

Views

Author

N. J. A. Sloane, Jan 05 2001

Keywords

Comments

In Table I of the Read-Wormald paper the c and d rows actually show double the numbers (Wormald). - Emeric Deutsch, Jan 26 2005

References

  • R. C. Read and N. C. Wormald, Number of labeled 4-regular graphs, J. Graph Theory, 4 (1980), 203-212.

Crossrefs

Cf. A005815, A058830, A058832, A058833, A058834, A058835, A058836, A058837.

Programs

  • Maple
    a[0]:=1: b[0]:=0: c[0]:=0: d[0]:=0: e[0]:=0: f[0]:=0: g[0]:=0: h[0]:=0: i[0]:=0: for p from 1 to 20 do a[p]:=((p-1)*(2*p-9)*a[p-1]+(2*p-8)*b[p-1]+c[p-1])/3: b[p]:=(6*p*(p-1)*a[p-1]+4*p*b[p-1]+p*d[p-1])/2: c[p]:=(6*p*(p-3)*b[p-1]+8*p*c[p-1]+4*p*d[p-1]+p*e[p-1])/4: d[p]:=p*b[p-1]+p*f[p-1]:e[p]:=(4*p*c[p-1]+4*p*d[p-1]+2*p*g[p-1]+p*(p-1)*(p-2)*a[p-3])/2:f[p]:=p*(p-1)*((4*p-8)*a[p-2]+2*b[p-2]+h[p-2])/2: g[p]:=p*(p-1)*(4*(p-3)*b[p-2]+4*c[p-2]+4*d[p-2]+2*f[p-2]+i[p-2])/2:h[p]:=p*((2*p-2)*a[p-1]+b[p-1]): i[p]:=p*((2*p-4)*b[p-1]+2*c[p-1]+2*d[p-1]+f[p-1]+h[p-1]): od: seq(c[n],n=0..20); # A058831(n)=c[n] - Emeric Deutsch, Jan 26 2005

Formula

Read and Wormald give recurrence relations involving all sequences A005815 and A058830-A058837 (see the Maple program). - Emeric Deutsch, Jan 26 2005

Extensions

More terms from Emeric Deutsch, Jan 26 2005

A058830 Number of labeled n-node 4-valent graphs containing a single double edge.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 90, 3150, 131040, 6667920, 416593800, 31506454980, 2841125225400, 301392906637680, 37173926260360890, 5276692469017119150, 854273993613848327520, 156491796247034356836000
Offset: 0

Views

Author

N. J. A. Sloane, Jan 05 2001

Keywords

References

  • R. C. Read and N. C. Wormald, Number of labeled 4-regular graphs, J. Graph Theory, 4 (1980), 203-212.

Crossrefs

Cf. A005815, A058831, A058832, A058833, A058834, A058835, A058836, A058837.

Programs

  • Maple
    a[0]:=1: b[0]:=0: c[0]:=0: d[0]:=0: e[0]:=0: f[0]:=0: g[0]:=0: h[0]:=0: i[0]:=0: for p from 1 to 20 do a[p]:=((p-1)*(2*p-9)*a[p-1]+(2*p-8)*b[p-1]+c[p-1])/3: b[p]:=(6*p*(p-1)*a[p-1]+4*p*b[p-1]+p*d[p-1])/2: c[p]:=(6*p*(p-3)*b[p-1]+8*p*c[p-1]+4*p*d[p-1]+p*e[p-1])/4: d[p]:=p*b[p-1]+p*f[p-1]:e[p]:=(4*p*c[p-1]+4*p*d[p-1]+2*p*g[p-1]+p*(p-1)*(p-2)*a[p-3])/2:f[p]:=p*(p-1)*((4*p-8)*a[p-2]+2*b[p-2]+h[p-2])/2: g[p]:=p*(p-1)*(4*(p-3)*b[p-2]+4*c[p-2]+4*d[p-2]+2*f[p-2]+i[p-2])/2:h[p]:=p*((2*p-2)*a[p-1]+b[p-1]): i[p]:=p*((2*p-4)*b[p-1]+2*c[p-1]+2*d[p-1]+f[p-1]+h[p-1]): od: seq(b[n],n=0..20); # A058830(n)=b[n] - Emeric Deutsch, Jan 26 2005

Formula

Read and Wormald give recurrence relations involving all sequences A005815 and A058830-A058837 (see the Maple program). - Emeric Deutsch, Jan 26 2005

Extensions

More terms from Emeric Deutsch, Jan 26 2005

A058833 Number of labeled n-node 4-valent graphs containing 3 double edges, a distinguished unordered pair of which are adjacent.

Original entry on oeis.org

0, 0, 0, 3, 0, 30, 360, 6930, 196728, 8115660, 433362960, 28552545945, 2276033387760, 216132739612218, 24118774853584320, 3125242929676107240, 465357404934002231280, 78908446775174591638440
Offset: 0

Views

Author

N. J. A. Sloane, Jan 05 2001

Keywords

References

  • R. C. Read and N. C. Wormald, Number of labeled 4-regular graphs, J. Graph Theory, 4 (1980), 203-212.

Crossrefs

Cf. A005815, A058830, A058831, A058832, A058834, A058835, A058836, A058837.

Programs

  • Maple
    a[0]:=1: b[0]:=0: c[0]:=0: d[0]:=0: e[0]:=0: f[0]:=0: g[0]:=0: h[0]:=0: i[0]:=0: for p from 1 to 20 do a[p]:=((p-1)*(2*p-9)*a[p-1]+(2*p-8)*b[p-1]+c[p-1])/3: b[p]:=(6*p*(p-1)*a[p-1]+4*p*b[p-1]+p*d[p-1])/2: c[p]:=(6*p*(p-3)*b[p-1]+8*p*c[p-1]+4*p*d[p-1]+p*e[p-1])/4: d[p]:=p*b[p-1]+p*f[p-1]:e[p]:=(4*p*c[p-1]+4*p*d[p-1]+2*p*g[p-1]+p*(p-1)*(p-2)*a[p-3])/2:f[p]:=p*(p-1)*((4*p-8)*a[p-2]+2*b[p-2]+h[p-2])/2: g[p]:=p*(p-1)*(4*(p-3)*b[p-2]+4*c[p-2]+4*d[p-2]+2*f[p-2]+i[p-2])/2:h[p]:=p*((2*p-2)*a[p-1]+b[p-1]): i[p]:=p*((2*p-4)*b[p-1]+2*c[p-1]+2*d[p-1]+f[p-1]+h[p-1]): od: seq(e[n],n=0..20); # A058833(n)=e[n] - Emeric Deutsch, Jan 26 2005

Formula

Read and Wormald give recurrence relations involving all sequences A005815 and A058830-A058837 (see the Maple program). - Emeric Deutsch, Jan 26 2005

Extensions

More terms from Emeric Deutsch, Jan 26 2005

A058834 Number of labeled n-node 4-valent graphs containing a triple edge.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 420, 16800, 763560, 43142400, 2979900000, 247022123040, 24219716320800, 2774585262168720, 367448041040780700, 55728771791388696000, 9599063849925363974160, 1863895566816244057824000
Offset: 0

Views

Author

N. J. A. Sloane, Jan 05 2001

Keywords

References

  • R. C. Read and N. C. Wormald, Number of labeled 4-regular graphs, J. Graph Theory, 4 (1980), 203-212.

Crossrefs

Cf. A005815, A058830, A058831, A058832, A058833, A058835, A058836, A058837.

Programs

  • Maple
    a[0]:=1: b[0]:=0: c[0]:=0: d[0]:=0: e[0]:=0: f[0]:=0: g[0]:=0: h[0]:=0: i[0]:=0: for p from 1 to 21 do a[p]:=((p-1)*(2*p-9)*a[p-1]+(2*p-8)*b[p-1]+c[p-1])/3: b[p]:=(6*p*(p-1)*a[p-1]+4*p*b[p-1]+p*d[p-1])/2: c[p]:=(6*p*(p-3)*b[p-1]+8*p*c[p-1]+4*p*d[p-1]+p*e[p-1])/4: d[p]:=p*b[p-1]+p*f[p-1]:e[p]:=(4*p*c[p-1]+4*p*d[p-1]+2*p*g[p-1]+p*(p-1)*(p-2)*a[p-3])/2:f[p]:=p*(p-1)*((4*p-8)*a[p-2]+2*b[p-2]+h[p-2])/2: g[p]:=p*(p-1)*(4*(p-3)*b[p-2]+4*c[p-2]+4*d[p-2]+2*f[p-2]+i[p-2])/2:h[p]:=p*((2*p-2)*a[p-1]+b[p-1]): i[p]:=p*((2*p-4)*b[p-1]+2*c[p-1]+2*d[p-1]+f[p-1]+h[p-1]): od: seq(f[n],n=0..21); # A058834(n)=f[n] - Emeric Deutsch, Jan 26 2005

Formula

Read and Wormald give recurrence relations involving all sequences A005815 and A058830-A058837 (see the Maple program). - Emeric Deutsch, Jan 26 2005

Extensions

More terms from Emeric Deutsch, Jan 26 2005

A058835 Number of labeled n-node 4-valent graphs containing a triple edge and a double edge.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 180, 3150, 105840, 4740120, 260366400, 17411708160, 1402666372800, 134317686068280, 15090968212259940, 1966411584852664950, 294177397021128260640, 50080787858122187821200
Offset: 0

Views

Author

N. J. A. Sloane, Jan 05 2001

Keywords

References

  • R. C. Read and N. C. Wormald, Number of labeled 4-regular graphs, J. Graph Theory, 4 (1980), 203-212.

Crossrefs

Cf. A005815, A058830, A058831, A058832, A058833, A058834, A058836, A058837.

Programs

  • Maple
    a[0]:=1: b[0]:=0: c[0]:=0: d[0]:=0: e[0]:=0: f[0]:=0: g[0]:=0: h[0]:=0: i[0]:=0: for p from 1 to 20 do a[p]:=((p - 1)*(2*p - 9)*a[p - 1] + (2*p - 8)*b[p - 1] + c[p - 1])/3: b[p]:=(6*p*(p - 1)*a[p - 1] + 4*p*b[p - 1] + p*d[p - 1])/2: c[p]:=(6*p*(p - 3)*b[p - 1] + 8*p*c[p - 1] + 4*p*d[p - 1] + p*e[p - 1])/4: d[p]:=p*b[p - 1] + p*f[p - 1]:e[p]:=(4*p*c[p - 1] + 4*p*d[p - 1] + 2*p*g[p - 1] + p*(p - 1)*(p - 2)*a[p - 3])/2:f[p]:=p*(p - 1)*((4*p - 8)*a[p - 2] + 2*b[p - 2] + h[p - 2])/2: g[p]:=p*(p - 1)*(4*(p - 3)*b[p - 2] + 4*c[p - 2] + 4*d[p - 2] + 2*f[p - 2] + i[p - 2])/2:h[p]:=p*((2*p - 2)*a[p - 1] + b[p - 1]): i[p]:=p*((2*p - 4)*b[p - 1] + 2*c[p - 1] + 2*d[p - 1] + f[p - 1] + h[p - 1]): od: seq(g[n],n=0..20); # A058835(n)=g[n] - Emeric Deutsch, Jan 26 2005

Formula

Read and Wormald give recurrence relations involving all sequences A005815 and A058830-A058837 (see the Maple program). - Emeric Deutsch, Jan 26 2005

Extensions

More terms from Emeric Deutsch, Jan 26 2005

A058836 Number of labeled n-node 4-valent graphs containing a loop.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 60, 1890, 77280, 3966480, 251067600, 19204305120, 1747829270880, 186823771322760, 23188769670126060, 3309132464435848050, 538177754986005214080, 98975242794632514448320
Offset: 0

Views

Author

N. J. A. Sloane, Jan 05 2001

Keywords

References

  • R. C. Read and N. C. Wormald, Number of labeled 4-regular graphs, J. Graph Theory, 4 (1980), 203-212.

Crossrefs

Cf. A005815, A058830, A058831, A058832, A058833, A058834, A058835, A058837.

Programs

  • Maple
    a[0]:=1: b[0]:=0: c[0]:=0: d[0]:=0: e[0]:=0: f[0]:=0: g[0]:=0: h[0]:=0: i[0]:=0: for p from 1 to 20 do a[p]:=((p-1)*(2*p-9)*a[p-1]+(2*p-8)*b[p-1]+c[p-1])/3: b[p]:=(6*p*(p-1)*a[p-1]+4*p*b[p-1]+p*d[p-1])/2: c[p]:=(6*p*(p-3)*b[p-1]+8*p*c[p-1]+4*p*d[p-1]+p*e[p-1])/4: d[p]:=p*b[p-1]+p*f[p-1]:e[p]:=(4*p*c[p-1]+4*p*d[p-1]+2*p*g[p-1]+p*(p-1)*(p-2)*a[p-3])/2:f[p]:=p*(p-1)*((4*p-8)*a[p-2]+2*b[p-2]+h[p-2])/2: g[p]:=p*(p-1)*(4*(p-3)*b[p-2]+4*c[p-2]+4*d[p-2]+2*f[p-2]+i[p-2])/2:h[p]:=p*((2*p-2)*a[p-1]+b[p-1]): i[p]:=p*((2*p-4)*b[p-1]+2*c[p-1]+2*d[p-1]+f[p-1]+h[p-1]): od: seq(h[n],n=0..20); # A058836(n)=h[n] - Emeric Deutsch, Jan 26 2005

Formula

Read and Wormald give recurrence relations involving all sequences A005815 and A058830-A058837 (see the Maple program). - Emeric Deutsch, Jan 26 2005

Extensions

More terms from Emeric Deutsch, Jan 26 2005

A058837 Number of labeled n-node 4-valent graphs containing a loop and a double edge.

Original entry on oeis.org

0, 0, 0, 0, 0, 30, 360, 12390, 492240, 24517080, 1499961960, 111400817220, 9894176455680, 1036335934435230, 126455286914316360, 17785504207015034490, 2856590783311452576480, 519670214181036892602720
Offset: 0

Views

Author

N. J. A. Sloane, Jan 05 2001

Keywords

References

  • R. C. Read and N. C. Wormald, Number of labeled 4-regular graphs, J. Graph Theory, 4 (1980), 203-212.

Crossrefs

Cf. A005815, A058830, A058831, A058832, A058833, A058834, A058835, A058836.

Programs

  • Maple
    a[0]:=1: b[0]:=0: c[0]:=0: d[0]:=0: e[0]:=0: f[0]:=0: g[0]:=0: h[0]:=0: i[0]:=0: for p from 1 to 20 do a[p]:=((p-1)*(2*p-9)*a[p-1]+(2*p-8)*b[p-1]+c[p-1])/3: b[p]:=(6*p*(p-1)*a[p-1]+4*p*b[p-1]+p*d[p-1])/2: c[p]:=(6*p*(p-3)*b[p-1]+8*p*c[p-1]+4*p*d[p-1]+p*e[p-1])/4: d[p]:=p*b[p-1]+p*f[p-1]:e[p]:=(4*p*c[p-1]+4*p*d[p-1]+2*p*g[p-1]+p*(p-1)*(p-2)*a[p-3])/2:f[p]:=p*(p-1)*((4*p-8)*a[p-2]+2*b[p-2]+h[p-2])/2: g[p]:=p*(p-1)*(4*(p-3)*b[p-2]+4*c[p-2]+4*d[p-2]+2*f[p-2]+i[p-2])/2:h[p]:=p*((2*p-2)*a[p-1]+b[p-1]): i[p]:=p*((2*p-4)*b[p-1]+2*c[p-1]+2*d[p-1]+f[p-1]+h[p-1]): od: seq(i[n],n=0..20); # A058837(n)=i[n] - Emeric Deutsch, Jan 26 2005

Formula

Read and Wormald give recurrence relations involving all sequences A005815 and A058830-A058837 (see the Maple program). - Emeric Deutsch, Jan 26 2005

Extensions

More terms from Emeric Deutsch, Jan 26 2005
Showing 1-8 of 8 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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