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 1-7 of 7 results.

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

A058832 Number of labeled n-node 4-valent graphs containing two adjacent double edges.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 630, 28560, 1330560, 74314800, 5057098200, 413836259760, 40145915529720, 4558576721418720, 599227672837944150, 90306248160926397600, 15470047011889029399840, 2989635481745274974582880
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

Links

Crossrefs

Cf. A005815, A058830, A058831, 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 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(d[n],n=0..21); # A058832(n)=d[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

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 1-7 of 7 results.

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

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