A302680 -id:A302680 - cp's OEIS frontend

A302674 Number of n X n 0..1 arrays with every element equal to 0, 1, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 3, 8, 20, 63, 453, 6311, 92889, 1847358, 65801890, 3339677315, 218906752065, 21593578996507, 3271858745091063, 693762002728416501, 208397398216895893003, 93110263365139995537485

Offset: 1

R. H. Hardin, Apr 11 2018

nonn

Diagonal of A302680.

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

R. H. Hardin, Table of n, a(n) for n = 1..20

Cf. A302680.

A302675 Number of nX3 0..1 arrays with every element equal to 0, 1, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

3, 3, 8, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349, 15127, 24476, 39603, 64079, 103682, 167761, 271443, 439204, 710647, 1149851, 1860498, 3010349, 4870847, 7881196, 12752043, 20633239, 33385282, 54018521

Offset: 1

R. H. Hardin, Apr 11 2018

nonn

Column 3 of A302680.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A302680.

Empirical: a(n) = a(n-1) +a(n-2) for n>5

A302676 Number of n X 4 0..1 arrays with every element equal to 0, 1, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

5, 5, 12, 20, 33, 64, 121, 231, 440, 838, 1597, 3042, 5796, 11042, 21037, 40079, 76357, 145473, 277150, 528017, 1005960, 1916521, 3651291, 6956316, 13252938, 25249049, 48103634, 91645416, 174599746, 332641529, 633737387, 1207375029, 2300250057, 4382358586

Offset: 1

R. H. Hardin, Apr 11 2018

nonn

Column 4 of A302680.

Empirical: The antidiagonal sums of A084534 lead to the terms of this sequence for n >= 5. - Johannes W. Meijer, Jun 17 2018

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A302680, A180662 (Kn11), A084534.

Empirical: a(n) = a(n-1) + 2*a(n-2) - a(n-4) for  n > 8.
Empirical g.f.: x*(5 - 3*x^2 - 2*x^3 - 6*x^4 - 4*x^5 + 3*x^6 + 2*x^7) / (1 - x - 2*x^2 + x^4). - Colin Barker, Jun 17 2018
The data in the range n = 6..210 is matched by h(n) = hypergeom([-n+1, -(1/2)*n, 1/4-(1/2)*n, -(1/2)*n+1/2, -(1/2)*n+3/4], [-n, -(2/3)*n+1, -(2/3)*n+2/3, -(2/3)*n+1/3], -256/27). - Peter Luschny, Aug 24 2018

A302677 Number of nX5 0..1 arrays with every element equal to 0, 1, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

8, 7, 18, 30, 63, 125, 257, 528, 1085, 2228, 4576, 9401, 19311, 39665, 81476, 167363, 343782, 706162, 1450533, 2979557, 6120333, 12571820, 25823881, 53045060, 108960300, 223816249, 459742831, 944361613, 1939821080, 3984602671

Offset: 1

R. H. Hardin, Apr 11 2018

nonn

Column 5 of A302680.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A302680.

Empirical: a(n) = a(n-1) +3*a(n-3) +2*a(n-4) +2*a(n-5) for n>10

A302678 Number of nX6 0..1 arrays with every element equal to 0, 1, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

13, 13, 40, 76, 187, 453, 1125, 2782, 6843, 16908, 41758, 103027, 254329, 627855, 1549720, 3825349, 9442726, 23308474, 57535003, 142020909, 350567119, 865346622, 2136039825, 5272643974, 13015100410, 32126739133, 79302295311, 195751392919

Offset: 1

R. H. Hardin, Apr 11 2018

nonn

Column 6 of A302680.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A302680.

Empirical: a(n) = a(n-1) +2*a(n-2) +4*a(n-3) +a(n-4) -2*a(n-5) -a(n-6) for n>12

A302679 Number of nX7 0..1 arrays with every element equal to 0, 1, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

21, 23, 94, 217, 661, 2013, 6311, 19497, 60253, 186797, 578385, 1790605, 5545571, 17172267, 53173813, 164661159, 509890659, 1578918645, 4889288817, 15140189411, 46883090855, 145178205375, 449559001303, 1392104734057, 4310792424591

Offset: 1

R. H. Hardin, Apr 11 2018

nonn

Column 7 of A302680.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A302680.

Empirical: a(n) = a(n-1) +a(n-2) +12*a(n-3) +14*a(n-4) +10*a(n-5) -9*a(n-6) -26*a(n-7) +2*a(n-8) +18*a(n-9) +6*a(n-10) -4*a(n-12) for n>19

A302681 Number of 3Xn 0..1 arrays with every element equal to 0, 1, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

4, 4, 8, 12, 18, 40, 94, 184, 358, 760, 1594, 3220, 6574, 13636, 28078, 57460, 118090, 243232, 499846, 1026496, 2110462, 4339696, 8918722, 18329596, 37680070, 77455324, 159200278, 327229276, 672635458, 1382602264, 2841890926, 5841485128

Offset: 1

R. H. Hardin, Apr 11 2018

nonn

Row 3 of A302680.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A302680.

Empirical: a(n) = a(n-1) +3*a(n-3) +3*a(n-4) for n>7

A302682 Number of 4Xn 0..1 arrays with every element equal to 0, 1, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

8, 6, 7, 20, 30, 76, 217, 509, 1189, 3034, 7569, 18274, 44932, 111561, 274057, 672217, 1657278, 4083105, 10038822, 24702412, 60827449, 149699125, 368356029, 906653234, 2231584641, 5492001706, 13516457764, 33267138281, 81875898241

Offset: 1

R. H. Hardin, Apr 11 2018

nonn

Row 4 of A302680.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A302680.

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

A302683 Number of 5Xn 0..1 arrays with every element equal to 0, 1, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

16, 9, 11, 33, 63, 187, 661, 1837, 5075, 15661, 46975, 135191, 398107, 1187251, 3492697, 10253381, 30301323, 89476359, 263483993, 776726391, 2291909243, 6757855265, 19921284797, 58748244533, 173250475905, 510831651353

Offset: 1

R. H. Hardin, Apr 11 2018

nonn

Row 5 of A302680.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A302680.

Empirical: a(n) = a(n-1) +a(n-2) +10*a(n-3) +13*a(n-4) -7*a(n-6) -6*a(n-7) -11*a(n-8) -6*a(n-9) -4*a(n-10) -2*a(n-11) for n>16

A302684 Number of 6Xn 0..1 arrays with every element equal to 0, 1, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

32, 14, 18, 64, 125, 453, 2013, 6725, 21745, 80985, 295335, 1015113, 3570091, 12835677, 45416833, 159687591, 566457119, 2010993911, 7108904181, 25146289499, 89111146015, 315554058131, 1116679458873, 3953641136991, 14000618548225

Offset: 1

R. H. Hardin, Apr 11 2018

nonn

Row 6 of A302680.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A302680.

Empirical: a(n) = a(n-1) +2*a(n-2) +18*a(n-3) +31*a(n-4) -4*a(n-5) -56*a(n-6) -58*a(n-7) -38*a(n-8) +52*a(n-9) +7*a(n-10) -47*a(n-11) +10*a(n-12) +a(n-13) -32*a(n-14) +12*a(n-15) +2*a(n-16) +8*a(n-17) for n>23

cp's OEIS Frontend

A302674 Number of n X n 0..1 arrays with every element equal to 0, 1, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A302675 Number of nX3 0..1 arrays with every element equal to 0, 1, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A302676 Number of n X 4 0..1 arrays with every element equal to 0, 1, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A302677 Number of nX5 0..1 arrays with every element equal to 0, 1, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A302678 Number of nX6 0..1 arrays with every element equal to 0, 1, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A302679 Number of nX7 0..1 arrays with every element equal to 0, 1, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A302681 Number of 3Xn 0..1 arrays with every element equal to 0, 1, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A302682 Number of 4Xn 0..1 arrays with every element equal to 0, 1, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A302683 Number of 5Xn 0..1 arrays with every element equal to 0, 1, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs