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 1-4 of 4 results.

A185899 1/8 the number of n X 2 0..7 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

Original entry on oeis.org

1, 15, 196, 2765, 38731, 545328, 7675381, 108065699, 1521488668, 21421955457, 301612441375, 4246586949080, 59790307544569, 841824567122343, 11852566615920436, 166879587240301061, 2349600516714827299
Offset: 1

Views

Author

R. H. Hardin, Feb 06 2011

Keywords

Comments

Column 2 of A185903.

Examples

			Some solutions for 3 X 2 with a(1,1)=0:
..0..1....0..0....0..6....0..0....0..0....0..0....0..0....0..0....0..0....0..7
..0..1....7..0....0..6....0..6....4..0....2..2....5..2....1..1....4..4....0..7
..1..1....7..7....5..5....6..6....4..0....3..3....5..2....3..3....1..1....7..7

Links

Crossrefs

Cf. A185903.

Formula

Empirical: a(n) = 13*a(n-1) + 27*a(n-2) - 147*a(n-3) - 245*a(n-4) - 343*a(n-5).
Empirical g.f.: x*(1 + 2*x - 26*x^2 - 41*x^3 - 56*x^4) / (1 - 13*x - 27*x^2 + 147*x^3 + 245*x^4 + 343*x^5). - Colin Barker, Apr 17 2018

A185900 1/8 the number of nX3 0..7 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

Original entry on oeis.org

1, 196, 7854, 546280, 28967421, 1748982326, 98953708266, 5781843976125, 332434487651623, 19267808077145684, 1112287426359828719, 64338491237732078416, 3717840477156798616939, 214944959102538319886245
Offset: 1

Views

Author

R. H. Hardin Feb 06 2011

Keywords

Comments

Column 3 of A185903

Examples

			Some solutions for 5X3 with a(1,1)=0
..0..4..0....0..4..0....0..4..4....0..4..0....0..4..0....0..0..0....0..0..0
..0..4..0....0..4..0....0..0..4....0..4..0....0..4..0....4..4..4....0..4..4
..2..4..4....2..2..2....2..2..4....4..6..6....2..2..2....6..0..0....0..2..2
..2..2..0....6..5..6....4..4..4....4..3..5....0..4..6....6..7..7....6..6..6
..0..0..0....6..5..6....2..2..2....4..3..5....0..4..6....6..2..2....2..2..6

Links

Formula

Empirical: a(n)=32*a(n-1)+1746*a(n-2)-10029*a(n-3)-277751*a(n-4)+323380*a(n-5)+6665171*a(n-6)-1880040*a(n-7)-2212279*a(n-8)-295754815*a(n-9)+974325088*a(n-10)-1138247283*a(n-11)-3413532399*a(n-12)-6260334885*a(n-13)+43564745112*a(n-14)+67448015978*a(n-15)-317297809157*a(n-16)+933625841547*a(n-17)+1754321298765*a(n-18)-4758109448687*a(n-19)-10555269100243*a(n-20)-10151918327418*a(n-21)-9040337868996*a(n-22)-20928026247912*a(n-23)

A185901 1/8 the number of nX4 0..7 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

Original entry on oeis.org

8, 2765, 546280, 139230658, 32611077940, 7921723799549, 1897334511466261, 457135757368429048, 109875454057222039886, 26435697398605508731039, 6357732815393016703934708, 1529282331683348275213637905
Offset: 1

Views

Author

R. H. Hardin Feb 06 2011

Keywords

Comments

Column 4 of A185903

Examples

			Some solutions for 3X4 with a(1,1)=0
..0..4..4..3....0..0..6..6....0..4..1..0....0..0..4..5....0..0..5..4
..0..0..1..3....2..0..3..3....0..4..1..0....4..0..4..5....0..6..5..4
..6..6..1..1....2..2..2..3....7..7..2..2....4..0..3..3....0..6..3..3

A185902 1/8 the number of nX5 0..7 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

Original entry on oeis.org

15, 38731, 28967421, 32611077940, 30884279980274
Offset: 1

Views

Author

R. H. Hardin Feb 06 2011

Keywords

Comments

Column 5 of A185903

Examples

			Some solutions for 3X5 with a(1,1)=0
..0..4..0..0..4....0..0..6..6..6....0..0..0..2..6....0..0..6..6..0
..0..4..6..0..4....4..4..4..0..0....0..4..4..2..6....4..4..4..0..0
..0..4..6..0..4....0..0..4..5..5....0..0..4..2..6....4..0..0..7..7
Showing 1-4 of 4 results.

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