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.

A183476 Number of n X 2 0..2 arrays with every element equal to either the sum mod 3 of its vertical neighbors or the sum mod 3 of its horizontal neighbors.

Original entry on oeis.org

3, 15, 39, 135, 495, 1647, 5751, 20223, 70119, 244863, 855927, 2985903, 10426887, 36416223, 127148535, 444006927, 1550518119, 5414352255, 18907098327, 66024403695, 230558764743, 805118884191, 2811503074743, 9817858453455
Offset: 1

Views

Author

R. H. Hardin, Jan 05 2011

Keywords

Comments

Column 2 of A183483.

Examples

			Some solutions for 4 X 2.
..2..2....2..2....1..1....0..0....2..2....0..0....0..0....2..2....0..0....1..1
..0..0....2..2....0..2....0..0....1..1....1..1....2..0....0..0....2..2....1..1
..1..1....0..0....2..1....1..1....0..0....1..1....2..0....2..2....1..1....2..2
..0..0....1..1....2..2....0..0....2..2....1..1....0..0....2..2....1..1....0..0
		

Crossrefs

Cf. A183483.

Formula

Empirical: a(n) = 3*a(n-1) + 12*a(n-3) - 18*a(n-4) - 36*a(n-6).
Empirical g.f.: 3*x*(1 + 2*x - 2*x^2 - 6*x^3 - 12*x^4 - 12*x^5) / ((1 - 6*x^3)*(1 - 3*x - 6*x^3)). - Colin Barker, Mar 29 2018

A183477 Number of nX3 0..2 arrays with every element equal to either the sum mod 3 of its vertical neighbors or the sum mod 3 of its horizontal neighbors.

Original entry on oeis.org

5, 39, 117, 587, 2925, 12131, 58333, 270611, 1220877, 5724163, 26403017, 121544939, 564597457, 2608586447, 12062272841, 55880316803, 258485374601, 1196311279235, 5538446306557, 25631318490835, 118643423750561, 549199683026799
Offset: 1

Views

Author

R. H. Hardin Jan 05 2011

Keywords

Comments

Column 3 of A183483

Examples

			Some solutions for 4X3
..1..1..0....1..1..1....0..2..2....1..1..0....1..1..0....2..2..0....1..1..0
..1..1..0....1..1..0....0..0..0....1..1..0....1..1..0....0..0..0....1..1..0
..1..1..0....2..2..2....1..0..2....0..0..0....2..2..0....1..0..0....0..0..0
..1..1..0....2..1..2....1..0..2....0..0..0....2..2..0....1..0..0....2..2..0
		

Formula

Empirical: a(n)=8*a(n-1)-18*a(n-2)+84*a(n-3)-579*a(n-4)+1348*a(n-5)-3464*a(n-6)+18376*a(n-7)-41015*a(n-8)+79527*a(n-9)-334512*a(n-10)+695496*a(n-11)-1111399*a(n-12)+3876831*a(n-13)-7441854*a(n-14)+10184221*a(n-15)-30655065*a(n-16)+54160710*a(n-17)-64701205*a(n-18)+173693460*a(n-19)-281900303*a(n-20)+296755925*a(n-21)-730333225*a(n-22)+1086432175*a(n-23)-1011789825*a(n-24)+2336474256*a(n-25)-3177451713*a(n-26)+2619035208*a(n-27)-5787685442*a(n-28)+7177420278*a(n-29)-5223552815*a(n-30)+11228646436*a(n-31)-12673488056*a(n-32)+8097165320*a(n-33)-17162050486*a(n-34)+17603349821*a(n-35)-9768296437*a(n-36)+20663234591*a(n-37)-19224576837*a(n-38)+9099536459*a(n-39)-19470134294*a(n-40)+16378130019*a(n-41)-6427344807*a(n-42)+14168986173*a(n-43)-10725609446*a(n-44)+3343950376*a(n-45)-7805973809*a(n-46)+5287675974*a(n-47)-1227503579*a(n-48)+3163113462*a(n-49)-1907177092*a(n-50)+293721475*a(n-51)-900778627*a(n-52)+482493019*a(n-53)-34626683*a(n-54)+165703644*a(n-55)-80150140*a(n-56)-3548276*a(n-57)-16126436*a(n-58)+7908948*a(n-59)+2463356*a(n-60)+267632*a(n-61)-411136*a(n-62)-464048*a(n-63)+49264*a(n-64)+9792*a(n-65)+28416*a(n-66)

A183478 Number of nX4 0..2 arrays with every element equal to either the sum mod 3 of its vertical neighbors or the sum mod 3 of its horizontal neighbors.

Original entry on oeis.org

7, 135, 587, 4015, 40073, 270549, 1942323, 15984991, 119888365, 894632985, 6977123487, 53362780811, 405255680609, 3117495042837, 23903072796727, 182681815961381, 1400954811635395, 10740879929227211, 82253911392409687
Offset: 1

Views

Author

R. H. Hardin Jan 05 2011

Keywords

Comments

Column 4 of A183483

Examples

			Some solutions for 6X4
..0..0..0..0....0..0..1..1....0..0..0..0....0..2..1..0....0..0..0..0
..2..2..0..2....1..0..1..1....1..2..0..0....0..2..1..0....0..0..1..1
..0..0..0..2....1..0..0..0....1..2..0..0....0..0..0..0....0..0..1..1
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..1..1....0..0..0..0
..0..0..0..2....2..1..2..2....0..0..0..2....0..0..0..0....1..1..0..1
..1..1..0..2....2..1..2..2....2..2..0..2....1..1..0..0....1..1..0..1
		

A183479 Number of nX5 0..2 arrays with every element equal to either the sum mod 3 of its vertical neighbors or the sum mod 3 of its horizontal neighbors.

Original entry on oeis.org

13, 495, 2925, 40073, 706473, 7773025, 107741253, 1577932971, 20728674493, 287526589977, 4036331530635, 55313628172919, 767230355186961, 10669808831015745, 147604547979187367, 2047336009619708185
Offset: 1

Views

Author

R. H. Hardin Jan 05 2011

Keywords

Comments

Column 5 of A183483

Examples

			Some solutions for 4X5
..1..1..0..1..1....1..0..0..0..0....1..1..0..0..0....2..2..0..1..1
..0..0..0..0..0....1..0..0..2..2....2..0..0..0..2....0..0..0..0..0
..0..2..1..0..1....0..0..0..0..0....1..2..0..0..2....1..2..2..2..0
..0..2..1..0..1....0..0..2..2..0....2..2..0..0..0....1..2..2..2..0
		

A183480 Number of nX6 0..2 arrays with every element equal to either the sum mod 3 of its vertical neighbors or the sum mod 3 of its horizontal neighbors.

Original entry on oeis.org

23, 1647, 12131, 270549, 7773025, 116198719, 2519745049, 56697667073, 1077056431167, 22884814320491, 486391513434439, 9923123962205421, 208990562982405425, 4391311455637955479, 91402396553197281527
Offset: 1

Views

Author

R. H. Hardin Jan 05 2011

Keywords

Comments

Column 6 of A183483

Examples

			Some solutions for 4X6
..0..2..2..0..1..1....0..0..0..0..1..1....0..1..1..2..1..2....0..0..0..0..0..1
..0..0..0..0..0..0....0..0..0..0..2..0....0..1..1..0..2..2....0..0..0..0..0..1
..0..0..0..0..1..0....1..2..1..0..1..2....0..2..2..0..0..0....1..0..2..2..0..0
..0..1..1..0..1..0....1..2..1..0..2..2....0..0..0..0..1..1....1..0..2..2..0..0
		

A183475 Number of n X n 0..2 arrays with every element equal to either the sum mod 3 of its vertical neighbors or the sum mod 3 of its horizontal neighbors.

Original entry on oeis.org

1, 15, 117, 4015, 706473, 116198719, 84056287173
Offset: 1

Views

Author

R. H. Hardin Jan 05 2011

Keywords

Comments

Diagonal of A183483

Examples

			Some solutions for 4X4
..0..1..1..0....0..0..0..0....2..0..1..0....2..1..2..1....0..0..2..2
..0..0..0..0....1..0..0..0....2..0..1..0....2..0..1..1....2..0..0..0
..2..0..1..2....1..0..0..1....0..0..0..0....0..0..0..0....2..0..0..0
..2..0..1..2....0..0..0..1....1..1..0..0....0..2..2..0....0..0..0..0
		

A183481 Number of nX7 0..2 arrays with every element equal to either the sum mod 3 of its vertical neighbors or the sum mod 3 of its horizontal neighbors.

Original entry on oeis.org

37, 5751, 58333, 1942323, 107741253, 2519745049, 84056287173
Offset: 1

Views

Author

R. H. Hardin Jan 05 2011

Keywords

Comments

Column 7 of A183483

Examples

			Some solutions for 4X7
..0..0..0..1..1..0..2....0..0..0..0..2..1..0....0..0..1..0..2..2..0
..0..0..0..1..0..0..2....0..0..0..0..2..1..0....0..0..1..0..0..0..0
..0..1..0..0..2..0..0....0..0..0..0..0..0..0....0..0..0..0..1..0..0
..0..1..0..2..2..0..0....0..0..0..0..0..2..2....0..1..1..0..1..0..0
		

A183482 Number of nX8 0..2 arrays with every element equal to either the sum mod 3 of its vertical neighbors or the sum mod 3 of its horizontal neighbors.

Original entry on oeis.org

63, 20223, 270611, 15984991, 1577932971, 56697667073
Offset: 1

Views

Author

R. H. Hardin Jan 05 2011

Keywords

Comments

Column 8 of A183483

Examples

			Some solutions for 4X8
..0..0..0..0..0..2..2..0....0..0..0..0..0..0..1..1....0..0..0..1..1..0..0..0
..0..0..0..0..0..0..0..0....0..0..0..0..0..0..0..2....0..0..0..0..0..0..1..1
..0..0..0..0..1..1..1..2....0..0..0..2..2..0..2..1....0..0..1..0..1..0..1..1
..0..1..1..0..1..1..1..2....0..0..0..2..2..0..2..2....0..0..1..0..1..0..1..1
		
Showing 1-8 of 8 results.