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 1-10 of 16 results. Next

A068722 Number of solenoidal flows (flow in = flow out) in a 3 X 3 square array with integer velocities -n .. n.

Original entry on oeis.org

1, 35, 247, 925, 2501, 5551, 10795, 19097, 31465, 49051, 73151, 105205, 146797, 199655, 265651, 346801, 445265, 563347, 703495, 868301, 1060501, 1282975, 1538747, 1830985, 2163001, 2538251, 2960335, 3432997, 3960125, 4545751, 5194051, 5909345, 6696097, 7558915
Offset: 0

Views

Author

R. H. Hardin, Feb 26 2002

Keywords

Comments

Conjecture: A255437(a(n)) = 2*n+1, i.e. a(n) = gives the position of the first occurrence of 2*n+1 in A255437. - Reinhard Zumkeller, Mar 23 2015

Examples

			Sample flows (. represents a space):
Numbers in long rows are on cell walls showing velocity rightward.
Numbers in long columns are on cell floors showing velocity downwards.
3 X 3 cell centers are at the intersection of long rows and long columns.
n=1:
.. 0 . 0 . 0
.0. -1. -1 . 0
.. 1 . 0. -1
.0 . 0 . 0 . 0
.. 1 . 0. -1
.0 . 1 . 1 . 0
.. 0 . 0 . 0
n=2:
.. 0 . 0 . 0
.0. -2. -1 . 0
.. 2. -1. -1
.0 . 0. -1 . 0
.. 2 . 0. -2
.0 . 2 . 2 . 0
.. 0 . 0 . 0

Links

Crossrefs

Cf. 2 X 2=1, 3, 5, 7..., 4 X 4 A068723, 5 X 5 A068724, 6x6 A068725, by velocity limit 1..13 A068726-A068738.
Cf. A016754, A255437.

Programs

Formula

a(n) = (1+2*n+2*n^2) * (1+3*n+3*n^2).
G.f.: (1+30*x+82*x^2+30*x^3+x^4)/(1-x)^5. - Colin Barker, Jul 30 2012
E.g.f.: exp(x)*(1 + 34*x + 89*x^2 + 48*x^3 + 6*x^4). - Stefano Spezia, Mar 10 2024

Extensions

Formula corrected by Colin Barker, Jul 30 2012

A068738 Number of solenoidal flows (flow in = flow out) in an n X n square array with integer velocities in -13 .. 13.

Original entry on oeis.org

1, 27, 199655, 547436323149, 535691029084640060219
Offset: 1

Views

Author

R. H. Hardin, Feb 26 2002

Keywords

Crossrefs

By size 3 X 3, ..., 6 X 6 A068722-A068725, by velocity limit 1..13 A068726-A068738.

Extensions

a(5) from Sean A. Irvine, Mar 10 2024

A068726 Number of solenoidal flows (flow in = flow out) in an n X n square array with integer velocities in -1 .. 1.

Original entry on oeis.org

1, 3, 35, 2053, 569397, 758541101, 4855339973053, 149596683621380451, 22207207625437795523567, 15894065026795563049567474623, 54873022990102933765115144179983347, 914167438412564688754864863927964270928677, 73512018227635160780006728165405332017240587741389
Offset: 1

Views

Author

R. H. Hardin, Feb 26 2002

Keywords

Crossrefs

By size 3 X 3, ..., 6 X 6 A068722-A068725, by velocity limit 1..13 A068726-A068738.

Extensions

a(12)-a(13) from Sean A. Irvine, Mar 06 2024

A068723 Number of solenoidal flows (flow in = flow out) in a 4 X 4 square array with integer velocities -n .. n.

Original entry on oeis.org

1, 2053, 160403, 3096791, 28905785, 173429597, 773568107, 2789847759, 8576204625, 23279942261, 57201104003, 129540052071, 274074872265, 547436323149, 1040787422427, 1895867410719, 3326525754145, 5647051042021, 9308792104563, 14946774417783, 23438233878745, 35975222324029, 54153684727627, 80081666851567, 116509584233329
Offset: 0

Views

Author

R. H. Hardin, Feb 26 2002

Keywords

Examples

			Sample flows (. represents a space):
Numbers in long rows are on cell walls showing velocity rightward.
Numbers in long columns are on cell floors showing velocity downwards.
4 X 4 cell centers are at the intersection of long rows and long columns.
n=1:
.. 0 . 0 . 0 . 0
.0. -1. -1. -1 . 0
.. 1 . 0 . 0. -1
.0 . 0. -1 . 0 . 0
.. 1 . 1. -1. -1
.0 . 0 . 1 . 0 . 0
.. 1 . 0 . 0. -1
.0 . 1 . 1 . 1 . 0
.. 0 . 0 . 0 . 0
n=2:
.. 0 . 0 . 0 . 0
.0. -2. -1. -2 . 0
.. 2. -1 . 1. -2
.0 . 0. -2 . 0 . 0
.. 2 . 1. -1. -2
.0 . 0 . 1 . 0 . 0
.. 2 . 0 . 0. -2
.0 . 2 . 2 . 2 . 0
.. 0 . 0 . 0 . 0

Links

Crossrefs

Cf. A005408 (2 X 2), A068722 (3 X 3), A068724 (5 X 5), A068725 (6 X 6).
By velocity limit 1..13 A068726-A068738.

Formula

Empirical G.f.: (x+1) * (x^8 + 2042*x^7 + 137876*x^6 + 1447150*x^5 + 3462710*x^4 + 1447150*x^3 + 137876*x^2 + 2042*x + 1) / (x-1)^10. [Colin Barker, Jul 31 2012]

Extensions

a(14)-a(24) from Sean A. Irvine, Mar 06 2024

A068724 Number of solenoidal flows (flow in = flow out) in a 5 X 5 square array with integer velocities -n .. n.

Original entry on oeis.org

1, 569397, 1305759171, 251611610655, 13336307324915, 322309309862183, 4598900066440609, 44976296745414509, 331136639667811845, 1954290045098180729, 9661874271897648847, 41320247284448146619, 156588834507399529975
Offset: 0

Views

Author

R. H. Hardin, Feb 26 2002

Keywords

Examples

			Sample flows (. represents a space):
Numbers in long rows are on cell walls showing velocity rightward.
Numbers in long columns are on cell floors showing velocity downwards.
5 X 5 cell centers are at the intersection of long rows and long columns.
n=1:
.. 0 . 0 . 0 . 0 . 0
.0. -1. -1. -1. -1 . 0
.. 1 . 0 . 0 . 0. -1
.0 . 0. -1. -1 . 0 . 0
.. 1 . 1 . 0. -1. -1
.0 . 0 . 0 . 0 . 0 . 0
.. 1 . 1 . 0. -1. -1
.0 . 0 . 1 . 1 . 0 . 0
.. 1 . 0 . 0 . 0. -1
.0 . 1 . 1 . 1 . 1 . 0
.. 0 . 0 . 0 . 0 . 0
n=2:
.. 0 . 0 . 0 . 0 . 0
.0. -2. -1. -1. -1 . 0
.. 2. -1 . 0 . 0. -1
.0 . 0. -2. -2. -1 . 0
.. 2 . 1 . 0. -1. -2
.0 . 0. -1. -1 . 0 . 0
.. 2 . 2 . 0. -2. -2
.0 . 0 . 2 . 2 . 0 . 0
.. 2 . 0 . 0 . 0. -2
.0 . 2 . 2 . 2 . 2 . 0
.. 0 . 0 . 0 . 0 . 0

Crossrefs

Cf. 2 X 2=1, 3, 5, 7..., 3 X 3 A068722, 4 X 4 A068723, 6x6 A068725, by velocity limit 1..13 A068726-A068738.

Extensions

a(6)-a(12) from Sean A. Irvine, Mar 06 2024

A068727 Number of solenoidal flows (flow in = flow out) in an n X n square array with integer velocities in -2 .. 2.

Original entry on oeis.org

1, 5, 247, 160403, 1305759171, 134771061592765, 176541437214450498265, 2940055615889904390546839103, 623112842926151670996790416231139397
Offset: 1

Views

Author

R. H. Hardin, Feb 26 2002

Keywords

Crossrefs

By size 3 X 3, ..., 6 X 6 A068722-A068725, by velocity limit 1..13 A068726-A068738.

Extensions

a(9) from Sean A. Irvine, Mar 08 2024

A068728 Number of solenoidal flows (flow in = flow out) in an n X n square array with integer velocities in -3 .. 3.

Original entry on oeis.org

1, 7, 925, 3096791, 251611610655, 500885416261650533, 24461989414349531084868443, 29358790904767905695470325002387331
Offset: 1

Views

Author

R. H. Hardin, Feb 26 2002

Keywords

Crossrefs

By size 3 X 3, ..., 6 X 6 A068722-A068725, by velocity limit 1..13 A068726-A068738.

Extensions

a(7)-a(8) from Sean A. Irvine, Mar 07 2024

A068729 Number of solenoidal flows (flow in = flow out) in an n X n square array with integer velocities in -4 .. 4.

Original entry on oeis.org

1, 9, 2501, 28905785, 13336307324915, 247753867499441888279, 185592614324336736251073584343
Offset: 1

Views

Author

R. H. Hardin, Feb 26 2002

Keywords

Crossrefs

By size 3 X 3, ..., 6 X 6 A068722-A068725, by velocity limit 1..13 A068726-A068738.

Extensions

a(6)-a(7) from Sean A. Irvine, Mar 08 2024

A068730 Number of solenoidal flows (flow in = flow out) in an n X n square array with integer velocities in -5 .. 5.

Original entry on oeis.org

1, 11, 5551, 173429597, 322309309862183, 35922392489639958547367
Offset: 1

Views

Author

R. H. Hardin, Feb 26 2002

Keywords

Crossrefs

By size 3 X 3, ..., 6 X 6 A068722-A068725, by velocity limit 1..13 A068726-A068738.

Extensions

a(6) from Sean A. Irvine, Mar 11 2024

A068731 Number of solenoidal flows (flow in = flow out) in an n X n square array with integer velocities in -6 .. 6.

Original entry on oeis.org

1, 13, 10795, 773568107, 4598900066440609, 2286173927365217148894607
Offset: 1

Views

Author

R. H. Hardin, Feb 26 2002

Keywords

Crossrefs

By size 3 X 3, ..., 6 X 6 A068722-A068725, by velocity limit 1..13 A068726-A068738.

Extensions

a(5)-a(6) from Sean A. Irvine, Mar 08 2024
Showing 1-10 of 16 results. Next

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