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 1-6 of 6 results.

A300203 Number of n X 3 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

4, 32, 248, 1933, 15070, 117494, 916061, 7142233, 55685704, 434163629, 3385035032, 26392036123, 205770269515, 1604325017633, 12508409345459, 97524069396190, 760363995846334, 5928315027859268, 46221177306565661, 360371745017815198
Offset: 1

Views

Author

R. H. Hardin, Feb 28 2018

Keywords

Comments

Column 3 of A300208.

Examples

			Some solutions for n=5;
  0 1 0    0 0 1    0 1 1    0 0 1    0 0 0    0 1 0    0 0 1
  1 0 0    0 1 1    1 0 1    1 0 0    1 1 0    0 0 1    0 1 0
  0 1 1    0 0 0    1 0 0    0 1 0    1 1 0    0 1 0    0 0 1
  1 1 1    0 1 1    1 1 1    1 0 0    0 0 1    1 0 1    0 0 0
  0 0 0    0 0 1    0 0 1    0 0 1    0 0 0    0 1 1    0 0 1
		

Crossrefs

Cf. A300208.

Formula

Empirical: a(n) = 8*a(n-1) - 2*a(n-2) + 5*a(n-3) - 13*a(n-4) - 6*a(n-5).
Empirical g.f.: -x*(-6*x^4-7*x^3+4)/(-6*x^5-13*x^4+5*x^3-2*x^2+8*x-1). - Simon Plouffe, Jun 20 2018

A300204 Number of nX4 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

8, 128, 1933, 29561, 451996, 6912249, 105708560, 1616600364, 24722667407, 378083758286, 5782035093260, 88424665581000, 1352278455547082, 20680395107688945, 316265292891587218, 4836645284923191877
Offset: 1

Views

Author

R. H. Hardin, Feb 28 2018

Keywords

Comments

Column 4 of A300208.

Examples

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

Crossrefs

Cf. A300208.

Formula

Empirical: a(n) = 15*a(n-1) +4*a(n-2) +22*a(n-3) -200*a(n-4) -372*a(n-5) +49*a(n-6) +405*a(n-7) +898*a(n-8) +427*a(n-9) -28*a(n-10) -359*a(n-11) -196*a(n-12) -30*a(n-13) +64*a(n-14) +24*a(n-15)

A300205 Number of n X 5 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

16, 512, 15070, 451996, 13548425, 406228452, 12180207076, 365209429387, 10950385677546, 328334797496128, 9844743765773028, 295183394744945449, 8850736864575395877, 265379233550361130727, 7957093141320853026332
Offset: 1

Views

Author

R. H. Hardin, Feb 28 2018

Keywords

Comments

Column 5 of A300208.

Examples

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

Crossrefs

Cf. A300208.

Formula

Empirical: a(n) = 30*a(n-1) -8*a(n-2) +343*a(n-3) -3214*a(n-4) -9170*a(n-5) -6989*a(n-6) -9332*a(n-7) +482996*a(n-8) +36160*a(n-9) +495066*a(n-10) -4606283*a(n-11) -2769327*a(n-12) +1332664*a(n-13) +25229638*a(n-14) +18945541*a(n-15) -24172763*a(n-16) -111255521*a(n-17) -63862029*a(n-18) +129871861*a(n-19) +300380879*a(n-20) +152885144*a(n-21) -339369704*a(n-22) -486006309*a(n-23) -128959877*a(n-24) +341481538*a(n-25) +413606386*a(n-26) +91315190*a(n-27) -187554462*a(n-28) -184211455*a(n-29) -33354181*a(n-30) +50022664*a(n-31) +38893772*a(n-32) +6506118*a(n-33) -4777876*a(n-34) -3960944*a(n-35) -936320*a(n-36) +381696*a(n-37) +156672*a(n-38).

A300206 Number of nX6 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

32, 2048, 117494, 6912249, 406228452, 23883950854, 1404241937017, 82562348427139, 4854250928660105, 285405606248444064, 16780418393854173458, 986604455823367492435, 58007394683107473100107, 3410543930287238106023455
Offset: 1

Views

Author

R. H. Hardin, Feb 28 2018

Keywords

Comments

Column 6 of A300208.

Examples

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

Crossrefs

Cf. A300208.

A300207 Number of nX7 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

64, 8192, 916061, 105708560, 12180207076, 1404241937017, 161892308617170, 18664492764362592, 2151821343856271110, 248082627699949131634, 28601348103095688080835, 3297438140691647751490978
Offset: 1

Views

Author

R. H. Hardin, Feb 28 2018

Keywords

Comments

Column 7 of A300208.

Examples

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

Crossrefs

Cf. A300208.

A300202 Number of n X n 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 8, 248, 29561, 13548425, 23883950854, 161892308617170, 4219465347519739696, 422854606293602673217071, 162939915121835846953153617510
Offset: 1

Views

Author

R. H. Hardin, Feb 28 2018

Keywords

Comments

Diagonal of A300208.

Examples

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

Crossrefs

Cf. A300208.
Showing 1-6 of 6 results.