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 1-5 of 5 results.

A268781 T(n,k) = Number of n X k binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two no more than once.

Original entry on oeis.org

2, 4, 4, 7, 11, 7, 13, 26, 26, 13, 23, 65, 91, 65, 23, 41, 148, 316, 316, 148, 41, 72, 343, 1031, 1462, 1031, 343, 72, 126, 766, 3354, 6383, 6383, 3354, 766, 126, 219, 1709, 10615, 27531, 38483, 27531, 10615, 1709, 219, 379, 3752, 33344, 115391, 224960
Offset: 1

Views

Author

R. H. Hardin, Feb 13 2016

Keywords

Comments

Table starts
...2....4......7......13........23.........41...........72...........126
...4...11.....26......65.......148........343..........766..........1709
...7...26.....91.....316......1031.......3354........10615.........33344
..13...65....316....1462......6383......27531.......115391........478849
..23..148...1031....6383.....38483.....224960......1288693.......7271509
..41..343...3354...27531....224960....1755113.....13493468.....101738555
..72..766..10615..115391...1288693...13493468....140404442....1425678976
.126.1709..33344..478849...7271509..101738555...1425678976...19400886875
.219.3752.103339.1957904..40511381..758303322..14341399141..262072220011
.379.8195.317958.7940136.223527424.5590121407.142487073304.3491534799847

Examples

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

Links

Crossrefs

Column 1 is A208354(n+1).
Diagonal is A143870.

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4).
k=2: a(n) = 2*a(n-1) +3*a(n-2) -4*a(n-3) -4*a(n-4).
k=3: a(n) = 4*a(n-1) +2*a(n-2) -16*a(n-3) -a(n-4) +12*a(n-5) -4*a(n-6).
k=4: [order 8].
k=5: [order 12].
k=6: [order 16].
k=7: [order 28].

A143875 Number of ways of placing kings with no more than 2 mutual attacks on an n X n chessboard.

Original entry on oeis.org

1, 2, 11, 155, 3280, 124511, 7623993, 795923016, 140176308483, 42642616703815
Offset: 0

Views

Author

R. H. Hardin, Sep 04 2008

Keywords

Crossrefs

Cf. A143870, A143881, A143886.
Cf. A143876, A143877, A143878, A143879, A143880.

A143881 Number of ways of placing kings with no more than 3 mutual attacks on an n X n chessboard.

Original entry on oeis.org

1, 2, 15, 207, 6084, 292607, 23511001, 3132847224, 693856861039, 259806377729539
Offset: 0

Views

Author

R. H. Hardin, Sep 04 2008

Keywords

Crossrefs

Cf. A143870, A143875, A143886.
Cf. A143882, A143883, A143884, A143885.

A143886 Number of ways of placing kings with no more than 4 mutual attacks on an n X n chessboard.

Original entry on oeis.org

1, 2, 15, 267, 9450, 577785, 58537749, 9751519234, 2673230750387, 1220300742842014
Offset: 0

Views

Author

R. H. Hardin, Sep 04 2008

Keywords

Crossrefs

Cf. A143870, A143875, A143881.
Cf. A143887, A143888, A143889, A143890, A143891, A143892, A143893.

A143892 Number of ways of placing kings with no more than 4 mutual attacks on an n X n chessboard symmetric under 90-degree rotation.

Original entry on oeis.org

1, 2, 1, 5, 6, 29, 47, 300, 665, 5276, 15554, 160307, 632041, 8448701, 44021226
Offset: 0

Views

Author

R. H. Hardin, Sep 04 2008

Keywords

Examples

			Example: for n=3 the a(3)=5 solutions are
. . .   . . .   K . K   K . K   . K .
. . .   . K .   . . .   . K .   K . K
. . .   . . .   K . K   K . K   . K .

Crossrefs

Cf. A143870, A143875, A143881, A143886.
Cf. A143886, A143887, A143888, A143889, A143890, A143891, A143893.
Showing 1-5 of 5 results.

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