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.

A282996 T(n,k) is the number of n X k 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors.

Original entry on oeis.org

2, 4, 4, 7, 11, 7, 13, 33, 33, 13, 24, 98, 163, 98, 24, 44, 291, 803, 803, 291, 44, 81, 865, 3971, 6547, 3971, 865, 81, 149, 2570, 19587, 53389, 53389, 19587, 2570, 149, 274, 7637, 96693, 435027, 720417, 435027, 96693, 7637, 274, 504, 22693, 477297, 3546870
Offset: 1

Views

Author

R. H. Hardin, Feb 26 2017

Keywords

Examples

			Table starts:
...2.....4........7.........13...........24.............44...............81
...4....11.......33.........98..........291............865.............2570
...7....33......163........803.........3971..........19587............96693
..13....98......803.......6547........53389.........435027..........3546870
..24...291.....3971......53389.......720417........9706901........130854309
..44...865....19587.....435027......9706901......216173426.......4817792042
..81..2570....96693....3546870....130854309.....4817792042.....177509416175
.149..7637...477297...28911809...1763845523...107354061547....6539125324144
.274.22693..2355925..235681253..23775564134..2392171690343..240894164469261
.504.67432.11629027.1921212987.320481684651.53305366529469.8874303766960833
Some solutions for n=5 and k=4:
..0..1..1..0. .0..0..1..0. .1..0..0..0. .0..0..0..0. .1..0..0..0
..0..0..0..1. .0..0..0..1. .0..1..0..0. .1..0..0..0. .0..1..0..1
..0..1..1..0. .1..0..0..0. .0..1..0..1. .0..1..0..1. .0..0..0..0
..0..0..0..0. .1..0..0..0. .0..0..1..0. .1..0..1..0. .0..0..0..0
..0..0..0..1. .0..0..1..0. .1..0..0..1. .0..0..0..0. .0..0..1..0

Links

Crossrefs

Columns are A000073(n+3), A282990, A282991, A282992, A282993, A282994, A282995.
Diagonal is A067968.

Formula

Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2) +a(n-3);
k=2: a(n) = 2*a(n-1) +3*a(n-2) -a(n-4);
k=3: [order 9];
k=4: [order 15];
k=5: [order 36];
k=6: [order 69].

A050974 Number of binary arrangements on n X n array without three adjacent 1's in a row or column.

Original entry on oeis.org

1, 2, 16, 265, 16561, 3157010, 1828904402, 3323590649777, 18691199385898465, 325778072452564800064, 17617718915229579206450786, 2954164381835835259001326344913, 1536134628973698280539373190731911729, 2477137610106747308204461168746042225266836, 12387488188151269567355592399321080831513078632498, 192102098800681202990688566451981906679020804069237862571, 9238409697848267958752630399467598421213391733838644131510525089
Offset: 0

Views

Author

Eric W. Weisstein

Keywords

References

  • Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 342-349.

Links

Crossrefs

Any connected three 1's gives A067968.
Cf. A006506. Diagonal of A202471.

Programs

  • Mathematica
    t[m_] := t[m] = Map[ArrayReshape[#, {m, m}] &, Tuples[{0, 1}, m^2]]; a[m_] := a[m] = Count[Table[AnyTrue[Flatten[{Table[Equal[1, t[m][[n, a, b]], t[m][[n, a, b + 1]], t[m][[n, a, b + 2]]], {a, 1, m}, {b, 1, m - 2}], Table[Equal[1, t[m][[n, a, b]], t[m][[n, a + 1, b]], t[m][[n, a + 2, b]]], {a, 1, m - 2}, {b, 1, m}]}], TrueQ], {n, 1, 2^(m^2)}], False]; (* Robert P. P. McKone, Jan 04 2022 *)

Extensions

More terms from R. H. Hardin, Feb 02 2002
a(0)=1 prepended and a(13)-a(16) from Peter J. Taylor, Sep 26 2024

A068471 Number of n X n binary matrices with each 1 having at most 2 adjacent 1's.

Original entry on oeis.org

1, 2, 16, 378, 30824, 8402216, 7664347268, 23371379782671, 238225926162821893, 8118262028301675826132, 924887563235974860108746534, 352261845112790535941917078458268
Offset: 0

Views

Author

R. H. Hardin, Mar 10 2002

Keywords

Crossrefs

No adjacent 1's A006506, one adjacent 1 A067968.

Extensions

a(0)=1 prepended by Alois P. Heinz, Sep 26 2024

A068472 Number of n X n binary matrices with every 1 having at most 3 adjacent 1's.

Original entry on oeis.org

1, 2, 16, 496, 58640, 26536192, 45851039232, 302758305892480, 7638804476736307712, 736437724731312162567680, 271287639195997221896855543808, 381862430868672544566361613406502912
Offset: 0

Views

Author

R. H. Hardin, Mar 10 2002

Keywords

Crossrefs

No adjacent 1's A006506, one adjacent 1 A067968.

Extensions

a(0)=1 prepended by Alois P. Heinz, Sep 26 2024
Showing 1-4 of 4 results.

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