A184548 -id:A184548 - cp's OEIS frontend

A184539 Number of (n+2)X(n+2) binary arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.

45, 193, 631, 1837, 5313, 16345, 54543, 194245, 719905, 2725367, 10430675, 40158073, 155173369, 601154073, 2333701711, 9075257125, 35345417073, 137846719279, 538258108483, 2104099248441, 8233431070825, 32247604093423

Offset: 1

R. H. Hardin Jan 16 2011

nonn

Diagonal of A184548

			Some solutions for 4X4
..0..0..1..1....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..1
..0..0..1..1....0..0..0..1....0..0..0..0....0..0..0..1....0..1..1..1
..1..1..0..1....0..0..1..1....0..0..1..1....0..0..0..1....0..1..1..1
..1..1..0..1....0..0..1..1....1..1..0..0....0..0..0..1....0..1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..68

A184540 Number of (n+2) X 3 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

Original entry on oeis.org

45, 89, 147, 220, 309, 415, 539, 682, 845, 1029, 1235, 1464, 1717, 1995, 2299, 2630, 2989, 3377, 3795, 4244, 4725, 5239, 5787, 6370, 6989, 7645, 8339, 9072, 9845, 10659, 11515, 12414, 13357, 14345, 15379, 16460, 17589, 18767, 19995, 21274, 22605, 23989

Offset: 1

R. H. Hardin, Jan 16 2011

nonn

Column 1 of A184548.

			Some solutions for 4 X 3:
..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..1..1....0..0..0....0..0..1....0..0..1....0..1..1....0..0..1
..0..1..1....0..1..1....0..0..1....1..1..1....0..1..1....0..1..1....1..1..0
..1..0..1....1..0..0....0..1..0....1..1..1....1..1..0....0..1..1....1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A184548.

Empirical: a(n) = (84 + 149*n + 36*n^2 + n^3) / 6. Corrected by Colin Barker, Apr 12 2018~
Conjectures from Colin Barker, Apr 12 2018: (Start)
G.f.: x*(45 - 91*x + 61*x^2 - 14*x^3) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
(End)

A184541 Number of (n+2) X 4 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

Original entry on oeis.org

89, 193, 340, 537, 792, 1114, 1513, 2000, 2587, 3287, 4114, 5083, 6210, 7512, 9007, 10714, 12653, 14845, 17312, 20077, 23164, 26598, 30405, 34612, 39247, 44339, 49918, 56015, 62662, 69892, 77739, 86238, 95425, 105337, 116012, 127489, 139808, 153010

Offset: 1

R. H. Hardin, Jan 16 2011

nonn

Column 2 of A184548.

			Some solutions for 6 X 4:
..0..0..0..0....0..0..0..1....0..0..0..0....0..0..0..1....0..0..0..1
..0..0..0..1....0..0..0..1....0..0..0..1....0..0..0..1....0..0..1..1
..0..0..0..1....0..0..0..1....0..0..0..1....0..0..0..1....0..1..1..1
..0..0..0..1....0..0..0..1....0..0..1..1....0..0..0..1....0..1..1..1
..0..0..1..0....0..0..1..0....0..1..0..0....0..0..0..1....1..1..1..1
..0..1..1..0....0..0..1..1....1..1..0..0....0..0..0..1....1..1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A184548.

Empirical: a(n) = (1/24)*n^4 + (3/4)*n^3 + (383/24)*n^2 + (201/4)*n + 22.
Conjectures from Colin Barker, Apr 12 2018: (Start)
G.f.: x*(89 - 252*x + 265*x^2 - 123*x^3 + 22*x^4) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)

A184542 Number of (n+2) X 5 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

Original entry on oeis.org

147, 340, 631, 1048, 1627, 2413, 3461, 4837, 6619, 8898, 11779, 15382, 19843, 25315, 31969, 39995, 49603, 61024, 74511, 90340, 108811, 130249, 155005, 183457, 216011, 253102, 295195, 342786, 396403, 456607, 523993, 599191, 682867, 775724, 878503

Offset: 1

R. H. Hardin, Jan 16 2011

nonn

Column 3 of A184548.

			Some solutions for 4 X 5:
..0..0..0..0..0....0..0..0..0..1....0..0..0..0..0....0..0..0..0..0
..0..0..0..1..1....0..0..0..0..1....0..0..0..1..1....0..0..0..0..1
..0..0..1..0..0....0..0..1..1..1....0..1..1..0..0....0..0..1..1..0
..0..0..1..1..1....0..1..1..1..1....1..1..1..1..1....0..1..1..1..0

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A184548.

Empirical: a(n) = (1/120)*n^5 + (5/24)*n^4 + (49/24)*n^3 + (739/24)*n^2 + (1659/20)*n + 31.
Conjectures from Colin Barker, Apr 13 2018: (Start)
G.f.: x*(147 - 542*x + 796*x^2 - 578*x^3 + 209*x^4 - 31*x^5) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>5.
(End)

A184543 Number of (n+2) X 6 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

Original entry on oeis.org

220, 537, 1048, 1837, 3024, 4774, 7307, 10909, 15944, 22867, 32238, 44737, 61180, 82536, 109945, 144737, 188452, 242861, 309988, 392133, 491896, 612202, 756327, 927925, 1131056, 1370215, 1650362, 1976953, 2355972, 2793964, 3298069, 3876057

Offset: 1

R. H. Hardin, Jan 16 2011

nonn

Column 4 of A184548.

			Some solutions for 4 X 6:
..0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..1..1....0..0..0..0..0..1
..0..0..0..0..0..1....0..0..0..0..0..1....0..0..0..0..1..1....0..0..0..0..0..1
..0..0..0..0..1..1....0..0..0..1..1..0....0..0..0..1..0..0....1..1..1..1..1..0
..0..1..1..1..1..0....1..1..1..1..1..0....1..1..1..1..1..1....1..1..1..1..1..0

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A184548.

Empirical: a(n) = (1/720)*n^6 + (11/240)*n^5 + (89/144)*n^4 + (209/48)*n^3 + (18317/360)*n^2 + (1231/10)*n + 41.
Conjectures from Colin Barker, Apr 13 2018: (Start)
G.f.: x*(220 - 1003*x + 1909*x^2 - 1922*x^3 + 1078*x^4 - 322*x^5 + 41*x^6) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)

A184544 Number of (n+2) X 7 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

Original entry on oeis.org

309, 792, 1627, 3024, 5313, 8989, 14767, 23648, 36997, 56634, 84939, 124972, 180609, 256695, 359215, 495484, 674357, 906460, 1204443, 1583256, 2060449, 2656497, 3395151, 4303816, 5413957, 6761534, 8387467, 10338132, 12665889, 15429643

Offset: 1

R. H. Hardin, Jan 16 2011

nonn

Column 5 of A184548.

			Some solutions for 4 X 7:
..0..0..0..0..0..0..0....0..0..0..0..0..0..0....0..0..1..1..1..1..1
..0..0..0..0..0..0..1....0..0..0..0..0..1..1....1..1..1..1..1..1..1
..0..0..0..0..0..1..1....0..0..1..1..1..0..0....1..1..1..1..1..1..1
..0..0..0..1..1..1..0....1..1..1..1..1..1..1....1..1..1..1..1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A184548.

Empirical: a(n) = (1/5040)*n^7 + (1/120)*n^6 + (53/360)*n^5 + (17/12)*n^4 + (5767/720)*n^3 + (3063/40)*n^2 + (11959/70)*n + 52.
Conjectures from Colin Barker, Apr 13 2018: (Start)
G.f.: x*(309 - 1680*x + 3943*x^2 - 5120*x^3 + 3955*x^4 - 1819*x^5 + 465*x^6 - 52*x^7) / (1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
(End)

A184545 Number of (n+2) X 8 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

Original entry on oeis.org

415, 1114, 2413, 4774, 8989, 16345, 28844, 49489, 82648, 134509, 213640, 331669, 504100, 751282, 1099549, 1582550, 2242789, 3133396, 4320151, 5883784, 7922575, 10555279, 13924402, 18199855, 23583014, 30311215, 38662714, 48962143, 61586494

Offset: 1

R. H. Hardin, Jan 16 2011

nonn

Column 6 of A184548.

			Some solutions for 4 X 8:
  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 0 0 0 0 1 1     0 0 0 0 0 0 0 0     0 0 0 0 0 0 1 1
  0 0 0 0 0 1 0 1     0 0 0 0 0 0 1 1     0 0 0 0 0 1 0 0
  0 0 0 1 1 1 1 1     0 0 0 1 1 1 0 0     0 0 0 0 0 1 1 1

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A184548.

Empirical: a(n) = (1/40320)*n^8 + (13/10080)*n^7 + (83/2880)*n^6 + (13/36)*n^5 + (15967/5760)*n^4 + (19201/1440)*n^3 + (121183/1120)*n^2 + (12673/56)*n + 64.
Conjectures from Colin Barker, Apr 13 2018: (Start)
G.f.: x*(415 - 2621*x + 7327*x^2 - 11699*x^3 + 11605*x^4 - 7310*x^5 + 2861*x^6 - 641*x^7 + 64*x^8) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
(End)

A184546 Number of (n+2) X 9 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

Original entry on oeis.org

539, 1513, 3461, 7307, 14767, 28844, 54543, 99872, 177207, 305112, 510719, 832788, 1325583, 2063717, 3148137, 4713439, 6936723, 10048219, 14343937, 20200617, 28093279, 38615698, 52504155, 70664842, 94205327, 124470514, 163083563

Offset: 1

R. H. Hardin, Jan 16 2011

nonn

Column 7 of A184548.

			Some solutions for 4 X 9:
..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..0....0..0..0..0..0..0..0..1..1
..0..0..0..0..0..0..0..0..0....0..0..1..1..1..1..1..0..1
..1..1..1..1..1..1..1..1..1....0..0..1..1..1..1..1..1..0

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A184548.

Empirical: a(n) = (1/362880)*n^9 + (1/5760)*n^8 + (289/60480)*n^7 + (217/2880)*n^6 + (12949/17280)*n^5 + (28049/5760)*n^4 + (468401/22680)*n^3 + (210319/1440)*n^2 + (145955/504)*n + 77.
Conjectures from Colin Barker, Apr 14 2018: (Start)
G.f.: x*(539 - 3877*x + 12586*x^2 - 23898*x^3 + 29072*x^4 - 23429*x^5 + 12502*x^6 - 4270*x^7 + 853*x^8 - 77*x^9) / (1 - x)^10.
a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.
(End)

A184547 Number of (n+2) X 10 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

Original entry on oeis.org

682, 2000, 4837, 10909, 23648, 49489, 99872, 194245, 364432, 660821, 1160932, 1981045, 3291704, 5338066, 8466235, 13156911, 20067894, 30087214, 44398911, 64563765, 92617576, 131189919, 183646650, 254259817, 348409036, 472818827

Offset: 1

R. H. Hardin, Jan 16 2011

nonn

Column 8 of A184548.

			Some solutions for 4 X 10:
..0..0..0..0..0..1..1..1..1..1....0..0..0..0..0..0..0..0..0..1
..0..0..1..1..1..1..1..1..1..1....0..0..0..0..0..0..0..0..0..1
..0..0..1..1..1..1..1..1..1..1....0..0..0..0..0..0..0..0..1..0
..1..1..1..1..1..1..1..1..1..1....0..0..0..0..0..1..1..1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A184548.

Empirical: a(n) = (1/3628800)*n^10 + (1/48384)*n^9 + (83/120960)*n^8 + (107/8064)*n^7 + (28573/172800)*n^6 + (5323/3840)*n^5 + (1434973/181440)*n^4 + (366371/12096)*n^3 + (2399357/12600)*n^2 + (151541/420)*n + 91.
Conjectures from Colin Barker, Apr 14 2018: (Start)
G.f.: x*(682 - 5502*x + 20347*x^2 - 44828*x^3 + 64744*x^4 - 63833*x^5 + 43442*x^6 - 20156*x^7 + 6118*x^8 - 1104*x^9 + 91*x^10) / (1 - x)^11.
a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>11.
(End)

cp's OEIS Frontend

A184539 Number of (n+2)X(n+2) binary arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.

Views

Author

Keywords

Comments

Examples

Links

A184540 Number of (n+2) X 3 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A184541 Number of (n+2) X 4 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A184542 Number of (n+2) X 5 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A184543 Number of (n+2) X 6 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A184544 Number of (n+2) X 7 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A184545 Number of (n+2) X 8 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A184546 Number of (n+2) X 9 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A184547 Number of (n+2) X 10 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula