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.

A298924 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 1, 1, 0, 4, 0, 1, 4, 4, 1, 0, 8, 1, 8, 0, 1, 32, 2, 2, 32, 1, 0, 32, 3, 3, 3, 32, 0, 1, 64, 5, 7, 7, 5, 64, 1, 0, 256, 8, 6, 9, 6, 8, 256, 0, 1, 256, 16, 9, 12, 12, 9, 16, 256, 1, 0, 512, 21, 20, 17, 19, 17, 20, 21, 512, 0, 1, 2048, 34, 22, 41, 22, 22, 41, 22, 34, 2048, 1, 0, 2048, 55, 35, 42
Offset: 1

Views

Author

R. H. Hardin, Jan 29 2018

Keywords

Comments

Table starts
.0...1..0..1..0..1..0...1...0...1....0....1....0.....1.....0.....1......0
.1...4..4..8.32.32.64.256.256.512.2048.2048.4096.16384.16384.32768.131072
.0...4..1..2..3..5..8..16..21..34...55...89..144...236...377...610....987
.1...8..2..3..7..6..9..20..22..35...59...90..145...240...378...611....991
.0..32..3..7..9.12.17..41..42..67..109..172..277...461...722..1167...1889
.1..32..5..6.12.19.22..48..53.103..169..272..446...863..1346..2395...4154
.0..64..8..9.17.22.31..83..92.172..309..549..923..1830..3021..5580..10091
.1.256.16.20.41.48.83.199.225.460..943.1570.2795..5933.10113.19462..37621
.0.256.21.22.42.53.92.225.330.644.1348.2306.4339..9315.17574.35170..70446

Examples

			Some solutions for n=5 k=4
..0..0..0..0. .0..0..1..1. .0..1..0..0. .0..0..0..0. .0..0..1..0
..0..0..0..0. .0..0..1..1. .0..1..0..0. .0..0..0..0. .0..0..1..0
..0..0..0..0. .0..0..1..1. .1..1..0..0. .0..0..0..0. .0..0..1..1
..1..1..1..1. .0..0..1..1. .0..1..0..0. .0..0..0..0. .0..0..1..0
..1..1..1..1. .0..0..1..1. .0..1..0..0. .0..0..0..0. .0..0..1..0

Links

Crossrefs

Column 2 is A096252(n-1).

Formula

Empirical for column k:
k=1: a(n) = a(n-2)
k=2: a(n) = 8*a(n-3)
k=3: a(n) = a(n-1) +a(n-2) +a(n-6) -a(n-7) -a(n-8)
k=4: a(n) = a(n-1) +a(n-2) +a(n-6) -a(n-7) -a(n-8)
k=5: a(n) = a(n-1) +a(n-2) +a(n-6) -a(n-7) -a(n-8) for n>11

A299451 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 3, 4, 3, 5, 4, 4, 5, 8, 8, 1, 8, 8, 13, 32, 4, 4, 32, 13, 21, 32, 10, 21, 10, 32, 21, 34, 64, 6, 32, 32, 6, 64, 34, 55, 256, 11, 36, 231, 36, 11, 256, 55, 89, 256, 41, 161, 163, 163, 161, 41, 256, 89, 144, 512, 24, 264, 546, 211, 546, 264, 24, 512, 144, 233, 2048, 42, 430
Offset: 1

Views

Author

R. H. Hardin, Feb 10 2018

Keywords

Comments

Table starts
..1...2..3...5....8...13....21.....34.....55......89......144.......233
..2...4..4...8...32...32....64....256....256.....512.....2048......2048
..3...4..1...4...10....6....11.....41.....24......42......169.......100
..5...8..4..21...32...36...161....264....430....1475.....2598......4872
..8..32.10..32..231..163...546...2904...2321....8729....37095.....34873
.13..32..6..36..163..211...804...3138...4869...21921....69029....124071
.21..64.11.161..546..804..6326..19745..39495..290364...855008...2191987
.34.256.41.264.2904.3138.19745.174794.205522.1778833.11489465..16992517
.55.256.24.430.2321.4869.39495.205522.665961.5936888.26103440.114805573

Examples

			Some solutions for n=5 k=4
..0..1..0..0. .0..0..1..1. .0..1..1..0. .0..0..0..1. .0..1..1..0
..1..1..1..1. .0..0..1..1. .1..0..1..1. .0..0..0..1. .0..1..1..0
..0..1..1..1. .0..0..0..0. .1..1..1..0. .1..1..0..0. .1..1..1..1
..1..1..0..0. .1..1..0..0. .0..1..1..1. .0..0..0..1. .1..0..0..1
..0..1..1..1. .1..1..0..0. .1..0..1..0. .0..0..0..1. .1..0..0..1

Links

Crossrefs

Column 1 is A000045(n+1).
Column 2 is A096252(n-1).

Formula

Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 8*a(n-3) for n>4
k=3: [order 18] for n>19
k=4: [order 62] for n>63

A300089 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 3, 4, 3, 5, 4, 4, 5, 8, 8, 1, 8, 8, 13, 32, 4, 4, 32, 13, 21, 32, 10, 25, 10, 32, 21, 34, 64, 6, 50, 50, 6, 64, 34, 55, 256, 19, 98, 415, 98, 19, 256, 55, 89, 256, 41, 359, 533, 533, 359, 41, 256, 89, 144, 512, 32, 766, 3089, 1822, 3089, 766, 32, 512, 144, 233, 2048, 106
Offset: 1

Views

Author

R. H. Hardin, Feb 24 2018

Keywords

Comments

Table starts
..1...2..3....5.....8.....13......21........34.........55..........89
..2...4..4....8....32.....32......64.......256........256.........512
..3...4..1....4....10......6......19........41.........32.........106
..5...8..4...25....50.....98.....359.......766.......1932........5677
..8..32.10...50...415....533....3089.....13808......27523......150838
.13..32..6...98...533...1822...13646.....64560.....292356.....1935206
.21..64.19..359..3089..13646..167131...1179926....7203918....75245386
.34.256.41..766.13808..64560.1179926..14634300..102798960..1708342471
.55.256.32.1932.27523.292356.7203918.102798960.1518807971.32115302281

Examples

			Some solutions for n=5 k=4
..0..0..1..1. .0..0..0..0. .0..0..1..1. .0..0..0..1. .0..0..1..1
..0..0..1..1. .0..0..0..0. .0..0..1..1. .0..0..0..1. .0..0..1..1
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .1..1..1..1
..0..0..0..0. .1..1..0..0. .1..1..0..0. .0..0..0..1. .1..1..1..1
..0..0..0..0. .1..1..0..0. .1..1..0..0. .0..0..0..1. .1..1..1..1

Links

Crossrefs

Column 1 is A000045(n+1).
Column 2 is A096252(n-1).

Formula

Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 8*a(n-3) for n>4
k=3: [order 20] for n>21
k=4: [order 59] for n>61

A137717 Hankel transform of A106191.

Original entry on oeis.org

1, -4, 4, 8, -32, 32, 64, -256, 256, 512, -2048, 2048, 4096, -16384, 16384, 32768, -131072, 131072, 262144, -1048576, 1048576, 2097152, -8388608, 8388608, 16777216, -67108864, 67108864, 134217728, -536870912, 536870912
Offset: 0

Views

Author

Paul Barry, Feb 08 2008

Keywords

Comments

Hankel transform of A132310. [From Paul Barry, Apr 26 2009]

Links

Crossrefs

Apart from signs, essentially the same as A096252.

Programs

  • Mathematica
    LinearRecurrence[{-2,-4},{1,-4},30] (* Harvey P. Dale, Oct 05 2017 *)

Formula

G.f.: (1-2x)/(1+2x+4x^2).
a(n)=Product{k=0..n, (3*cos(2*pi*(k-1)/3)/2-5/4-2*0^k)^(n-k)};
a(n) = 2^n*A061347(n+2) = -2a(n-1)-4a(n-2). - R. J. Mathar, Feb 21 2008
Showing 1-4 of 4 results.

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