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 11 results. Next

A067963 Number of binary arrangements without adjacent 1's on n X n array connected e-w ne-sw nw-se.

Original entry on oeis.org

2, 7, 77, 1152, 56549, 3837761, 806190208, 251170142257, 223733272186825, 319544298135448960, 1210302996752248488817, 7876274672755293629849313, 127662922218147601317696761088, 3758866349549535184419575245899295
Offset: 1

Views

Author

R. H. Hardin, Feb 02 2002

Keywords

Examples

			Neighbors for n=4 (dots represent spaces):
. o--o--o--o
...\/ \/ \/
.../\ /\ /\
. o--o--o--o
...\/ \/ \/
.../\ /\ /\
. o--o--o--o
...\/ \/ \/
.../\ /\ /\
. o--o--o--o

Links

Crossrefs

Cf. circle A000204, line A000045, arrays: ne-sw nw-se A067965, n-s nw-se A067964, e-w n-s nw-se A066864, e-w ne-sw n-s nw-se A063443, n-s A067966, e-w n-s A006506, nw-se A067962, toruses: bare A002416, ne-sw nw-se A067960, ne-sw n-s nw-se A067959, e-w ne-sw n-s nw-se A067958, n-s A067961, e-w n-s A027683, e-w ne-sw n-s A066866.
Diagonal of A228683

Extensions

Terms a(15)-a(19) from Vaclav Kotesovec, May 01 2012

A228678 Number of nX3 binary arrays with no two ones adjacent horizontally, diagonally or antidiagonally.

Original entry on oeis.org

5, 19, 77, 313, 1277, 5215, 21305, 87049, 355685, 1453363, 5938613, 24265921, 99153677, 405154783, 1655515121, 6764650225, 27641241413, 112945711027, 461510880221, 1885793543785, 7705597945181, 31486076453887, 128656207802537
Offset: 1

Views

Author

R. H. Hardin Aug 30 2013

Keywords

Comments

Column 3 of A228683

Examples

			Some solutions for n=4
..1..0..1....1..0..0....0..1..0....0..0..1....0..1..0....0..0..1....0..0..0
..1..0..0....1..0..1....0..0..0....0..0..0....0..0..0....0..0..1....0..0..0
..1..0..1....0..0..1....0..1..0....1..0..0....1..0..0....0..0..0....0..0..0
..1..0..0....1..0..0....0..0..0....1..0..1....1..0..1....0..0..0....0..1..0

Links

Formula

Empirical: a(n) = 5*a(n-1) -3*a(n-2) -3*a(n-3).
Empirical: G.f. -x*(-5+6*x+3*x^2) / ( 1-5*x+3*x^2+3*x^3 ). - R. J. Mathar, Aug 31 2013

A228679 Number of nX4 binary arrays with no two ones adjacent horizontally, diagonally or antidiagonally.

Original entry on oeis.org

8, 40, 216, 1152, 6160, 32928, 176032, 941056, 5030848, 26894720, 143778176, 768632832, 4109082880, 21967006208, 117434808832, 627802177536, 3356207397888, 17942161561600, 95918137153536, 512774840614912
Offset: 1

Views

Author

R. H. Hardin Aug 30 2013

Keywords

Comments

Column 4 of A228683

Examples

			Some solutions for n=4
..0..0..1..0....0..1..0..1....1..0..0..0....0..0..0..1....1..0..0..1
..0..0..0..0....0..0..0..1....0..0..0..1....1..0..0..0....1..0..0..0
..1..0..1..0....1..0..0..0....0..0..0..1....1..0..0..1....0..0..0..0
..1..0..1..0....0..0..0..0....1..0..0..1....1..0..0..0....1..0..0..0

Links

Formula

Empirical: a(n) = 6*a(n-1) -2*a(n-2) -8*a(n-3).
Empirical: G.f. -8*x*(-1+x+x^2) / ( 1-6*x+2*x^2+8*x^3 ). - R. J. Mathar, Aug 31 2013

A228680 Number of n X 5 binary arrays with no two ones adjacent horizontally, diagonally or antidiagonally.

Original entry on oeis.org

13, 97, 809, 6737, 56549, 475809, 4008817, 33795201, 284980061, 2403420097, 20270798553, 170971640209, 1442058561397, 12163101107393, 102590452275041, 865306832676993, 7298499493581101, 61559793235182241, 519231197740651273
Offset: 1

Views

Author

R. H. Hardin, Aug 30 2013

Keywords

Comments

Column 5 of A228683.

Examples

			Some solutions for n=4:
..0..0..1..0..0....0..0..0..0..0....0..0..1..0..0....0..1..0..0..1
..0..0..0..0..1....0..0..1..0..1....0..0..0..0..1....0..0..0..0..1
..1..0..0..0..0....0..0..0..0..0....1..0..0..0..1....0..0..0..0..1
..0..0..1..0..0....0..0..0..0..1....0..0..0..0..0....1..0..0..0..0

Links

Crossrefs

Cf. A228683.

Formula

Empirical: a(n) = 12*a(n-1) -27*a(n-2) -32*a(n-3) +49*a(n-4) +20*a(n-5) -5*a(n-6).
Empirical g.f.: -x*(-13+59*x+4*x^2-64*x^3-15*x^4+5*x^5) / ( 1-12*x+27*x^2+32*x^3-49*x^4-20*x^5+5*x^6 ). - R. J. Mathar, Sep 02 2013

A228681 Number of n X 6 binary arrays with no two ones adjacent horizontally, diagonally or antidiagonally.

Original entry on oeis.org

21, 217, 2529, 28977, 333517, 3837761, 44171841, 508425617, 5852202757, 67361890809, 775372578689, 8924976046401, 102731553583965, 1182498825731233, 13611237290882689, 156673123529460833, 1803397245448244085
Offset: 1

Views

Author

R. H. Hardin, Aug 30 2013

Keywords

Examples

			Some solutions for n=4:
..0..0..0..0..0..0....0..0..0..1..0..0....0..0..0..1..0..0....1..0..1..0..1..0
..1..0..0..1..0..0....0..1..0..1..0..1....0..0..0..0..0..1....0..0..0..0..0..0
..0..0..0..0..0..1....0..0..0..0..0..1....1..0..0..0..0..0....1..0..1..0..0..0
..1..0..0..0..0..0....0..0..0..0..0..1....0..0..1..0..1..0....1..0..0..0..1..0

Links

Crossrefs

Column 6 of A228683.

Formula

Empirical: a(n) = 14*a(n-1) - 17*a(n-2) - 142*a(n-3) + 59*a(n-4) + 352*a(n-5) + 103*a(n-6) - 48*a(n-7).
Empirical g.f.: x*(21 - 77*x - 152*x^2 + 242*x^3 + 407*x^4 + 55*x^5 - 48*x^6) / (1 - 14*x + 17*x^2 + 142*x^3 - 59*x^4 - 352*x^5 - 103*x^6 + 48*x^7). - Colin Barker, Sep 12 2018

A228682 Number of nX7 binary arrays with no two ones adjacent horizontally, diagonally or antidiagonally.

Original entry on oeis.org

34, 508, 8832, 152048, 2644336, 46125216, 806190208, 14105294112, 246929287360, 4324094979072, 75733743499264, 1326545935320192, 23236786328620160, 407043788171511808, 7130373880883372800, 124906998542616448512
Offset: 1

Views

Author

R. H. Hardin Aug 30 2013

Keywords

Comments

Column 7 of A228683

Examples

			Some solutions for n=4
..0..0..1..0..1..0..0....0..0..0..0..1..0..0....0..0..1..0..0..0..0
..1..0..0..0..0..0..1....0..0..1..0..1..0..0....1..0..0..0..1..0..1
..1..0..1..0..0..0..1....0..0..1..0..0..0..0....1..0..1..0..1..0..0
..1..0..0..0..0..0..1....1..0..1..0..0..0..1....1..0..1..0..0..0..1

Links

Formula

Empirical: a(n) = 30*a(n-1) -226*a(n-2) -108*a(n-3) +4324*a(n-4) -1612*a(n-5) -27016*a(n-6) -2240*a(n-7) +50112*a(n-8) +20032*a(n-9) -16768*a(n-10) -4864*a(n-11) +2048*a(n-12)

A228684 Number of 3 X n binary arrays with no two ones adjacent horizontally, diagonally or antidiagonally.

Original entry on oeis.org

8, 17, 77, 216, 809, 2529, 8832, 28793, 97933, 324464, 1092561, 3642241, 12217528, 40825697, 136745357, 457357256, 1531058169, 5122533089, 17144628912, 57369165513, 191993439053, 642478726624, 2150072260001, 7195049684481
Offset: 1

Views

Author

R. H. Hardin, Aug 30 2013

Keywords

Examples

			Some solutions for n=4:
..0..0..0..1....0..0..0..0....0..0..0..0....1..0..1..0....0..1..0..0
..1..0..0..0....1..0..1..0....0..1..0..0....1..0..0..0....0..0..0..0
..1..0..1..0....0..0..0..0....0..0..0..1....0..0..0..1....1..0..1..0

Links

Crossrefs

Row 3 of A228683.

Formula

Empirical: a(n) = 2*a(n-1) + 6*a(n-2) - 5*a(n-3).
Empirical g.f.: x*(8 + x - 5*x^2) / (1 - 2*x - 6*x^2 + 5*x^3). - Colin Barker, Sep 12 2018

A228685 Number of 4 X n binary arrays with no two ones adjacent horizontally, diagonally or antidiagonally.

Original entry on oeis.org

16, 41, 313, 1152, 6737, 28977, 152048, 699833, 3508329, 16628064, 81753697, 392401121, 1913315024, 9233466953, 44861599897, 217002245696, 1052716150641, 5097234627985, 24711403148208, 119703506867161, 580159930998217
Offset: 1

Views

Author

R. H. Hardin, Aug 30 2013

Keywords

Examples

			Some solutions for n=4:
..0..1..0..1....1..0..0..0....0..1..0..0....0..0..1..0....1..0..0..0
..0..0..0..1....0..0..0..0....0..0..0..0....0..0..1..0....0..0..1..0
..0..1..0..0....1..0..0..0....1..0..0..0....0..0..1..0....0..0..0..0
..0..0..0..1....1..0..0..0....1..0..0..1....1..0..0..0....0..1..0..1

Links

Crossrefs

Row 4 of A228683.

Formula

Empirical: a(n) = 2*a(n-1) + 16*a(n-2) - 7*a(n-3) - 18*a(n-4).
Empirical g.f.: x*(1 + x)*(16 - 7*x - 18*x^2) / (1 - 2*x - 16*x^2 + 7*x^3 + 18*x^4). - Colin Barker, Sep 12 2018

A228686 Number of 5 X n binary arrays with no two ones adjacent horizontally, diagonally or antidiagonally.

Original entry on oeis.org

32, 99, 1277, 6160, 56549, 333517, 2644336, 17124415, 127116873, 859773376, 6193234393, 42741157353, 303661236672, 2115245880075, 14933039299621, 104468526402928, 735366366459485, 5154677670070421, 36235570461792016
Offset: 1

Views

Author

R. H. Hardin, Aug 30 2013

Keywords

Examples

			Some solutions for n=4:
..0..0..0..0....0..0..0..1....1..0..1..0....0..1..0..1....0..0..0..0
..0..0..0..1....0..0..0..1....0..0..1..0....0..1..0..1....1..0..0..0
..0..1..0..1....0..0..0..0....1..0..0..0....0..0..0..1....0..0..1..0
..0..1..0..0....1..0..0..0....0..0..0..1....1..0..0..1....1..0..1..0
..0..0..0..0....0..0..0..1....0..0..0..0....0..0..0..0....0..0..1..0

Links

Crossrefs

Row 5 of A228683.

Formula

Empirical: a(n) = 4*a(n-1) + 34*a(n-2) - 76*a(n-3) - 134*a(n-4) + 258*a(n-5) + 45*a(n-6) - 102*a(n-7).
Empirical g.f.: x*(32 - 29*x - 207*x^2 + 118*x^3 + 303*x^4 - 57*x^5 - 102*x^6) / (1 - 4*x - 34*x^2 + 76*x^3 + 134*x^4 - 258*x^5 - 45*x^6 + 102*x^7). - Colin Barker, Sep 12 2018

A228687 Number of 6Xn binary arrays with no two ones adjacent horizontally, diagonally or antidiagonally.

Original entry on oeis.org

64, 239, 5215, 32928, 475809, 3837761, 46125216, 419022831, 4618533791, 44467300608, 470238325217, 4657579001857, 48279924803328, 484835649414511, 4977465842992607, 50320320341072096, 514193976056767137
Offset: 1

Views

Author

R. H. Hardin Aug 30 2013

Keywords

Comments

Row 6 of A228683

Examples

			Some solutions for n=4
..0..0..0..0....1..0..0..0....0..0..1..0....1..0..0..0....0..1..0..1
..1..0..1..0....1..0..1..0....1..0..1..0....0..0..0..0....0..0..0..0
..1..0..1..0....1..0..1..0....1..0..0..0....1..0..0..0....0..1..0..1
..0..0..0..0....0..0..0..0....1..0..0..1....0..0..0..1....0..0..0..1
..0..0..0..1....0..0..0..0....1..0..0..1....0..0..0..1....0..0..0..1
..0..0..0..1....0..0..0..1....1..0..0..1....1..0..0..1....1..0..0..1

Links

Formula

Empirical: a(n) = 4*a(n-1) +88*a(n-2) -138*a(n-3) -1388*a(n-4) +1332*a(n-5) +5911*a(n-6) -2920*a(n-7) -8340*a(n-8) +816*a(n-9) +2232*a(n-10)
Showing 1-10 of 11 results. Next

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