A224158 -id:A224158 - cp's OEIS frontend

A224152 Number of n X n 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

2, 12, 89, 574, 3469, 20065, 114537, 650819, 3705824, 21181267, 121617211, 701255335, 4058735341, 23565789117, 137190976378, 800437914689, 4678794395883, 27391873966579, 160581355210547, 942493889605853

Offset: 1

R. H. Hardin, Mar 31 2013

nonn

Diagonal of A224158.

			Some solutions for n=3
..0..0..0....1..1..0....1..0..0....0..0..0....1..1..0....0..1..0....0..0..0
..0..0..0....1..1..0....0..1..0....0..0..0....1..0..0....1..1..1....0..1..0
..1..0..0....1..0..0....1..0..0....0..0..1....0..1..0....1..1..1....1..0..0

R. H. Hardin, Table of n, a(n) for n = 1..23

Cf. A224158.

A224153 Number of n X 3 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

7, 28, 89, 281, 900, 2935, 9681, 32020, 105937, 350311, 1157860, 3826287, 12643725, 41780500, 138063433, 456233915, 1507641652, 4982061047, 16463412165, 54403960596, 179779885769, 594089193379, 1963189403076, 6487431018743

Offset: 1

R. H. Hardin, Mar 31 2013

nonn

Column 3 of A224158.

			Some solutions for n=3:
..0..1..0....0..0..0....0..0..0....1..0..0....0..0..0....0..0..0....0..1..0
..1..1..1....1..0..0....1..1..0....0..1..1....1..0..0....1..1..1....1..1..0
..1..1..1....1..1..1....1..1..0....1..1..0....0..1..0....1..1..1....1..0..0

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

Cf. A224158.

Empirical: a(n) = 4*a(n-1) - 2*a(n-2) - a(n-3) - 4*a(n-4) + 14*a(n-5) - 2*a(n-6) - 2*a(n-9).

Empirical g.f.: x*(7 - 9*x^2 - 12*x^3 + 10*x^4 - 2*x^8) / (1 - 4*x + 2*x^2 + x^3 + 4*x^4 - 14*x^5 + 2*x^6 + 2*x^9). - Colin Barker, Aug 28 2018

A224154 Number of nX4 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

11, 56, 187, 574, 1783, 5657, 18408, 61140, 205390, 694018, 2350061, 7961090, 26964678, 91303265, 309082754, 1046163241, 3540718751, 11983122960, 40555030532, 137252283821, 464510611475, 1572073476421, 5320479934245

Offset: 1

R. H. Hardin Mar 31 2013

nonn

Column 4 of A224158

			Some solutions for n=3
..0..0..0..0....1..1..0..0....1..1..1..0....1..1..1..1....0..1..0..0
..1..0..0..0....1..1..0..0....1..1..0..0....1..1..1..1....1..1..1..0
..1..1..1..1....1..1..1..0....1..1..1..0....1..1..1..0....1..1..0..0

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

Empirical: a(n) = 5*a(n-1) -5*a(n-2) -2*a(n-3) -3*a(n-4) +18*a(n-5) -18*a(n-6) +27*a(n-7) -3*a(n-8) -4*a(n-9) -8*a(n-11) -6*a(n-12) -6*a(n-13) for n>14

A224155 Number of nX5 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

16, 101, 373, 1156, 3469, 10562, 32910, 105020, 342575, 1136503, 3815322, 12904448, 43836891, 149266926, 508857756, 1735637682, 5921189882, 20201365165, 68920464104, 235127759007, 802136163910, 2736424196762, 9334965911219

Offset: 1

R. H. Hardin Mar 31 2013

nonn

Column 5 of A224158

			Some solutions for n=3
..1..1..0..0..0....1..0..0..0..0....1..0..0..0..0....0..1..0..0..0
..1..1..1..0..0....0..0..0..0..0....0..1..0..0..0....1..1..1..0..0
..1..1..1..1..1....0..0..0..1..0....1..0..0..0..0....1..1..0..0..0

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

Empirical: a(n) = 6*a(n-1) -9*a(n-2) -a(n-3) +a(n-4) +23*a(n-5) -38*a(n-6) +42*a(n-7) -41*a(n-8) +89*a(n-9) -67*a(n-10) -9*a(n-11) +5*a(n-12) -32*a(n-13) -50*a(n-14) -12*a(n-15) -58*a(n-16) -28*a(n-17) +12*a(n-18) +4*a(n-20) for n>22

A224156 Number of nX6 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

22, 169, 702, 2271, 6786, 20065, 60214, 184233, 575410, 1833641, 5947567, 19579806, 65205152, 219009930, 740080588, 2511332286, 8545644419, 29133026750, 99436525669, 339656225391, 1160767044395, 3968114261421, 13567722769117

Offset: 1

R. H. Hardin Mar 31 2013

nonn

Column 6 of A224158

			Some solutions for n=3
..0..0..0..1..1..0....0..0..0..0..0..0....1..0..0..0..0..0....0..0..0..1..0..0
..0..0..1..1..1..0....0..0..1..1..1..1....0..0..0..0..0..0....1..1..1..1..0..0
..0..1..1..1..0..0....1..1..1..1..1..1....0..0..0..0..1..0....1..1..1..0..0..0

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

Empirical: a(n) = 7*a(n-1) -14*a(n-2) +3*a(n-3) +7*a(n-4) +24*a(n-5) -58*a(n-6) +62*a(n-7) -67*a(n-8) +112*a(n-9) -164*a(n-10) +193*a(n-11) -92*a(n-12) -46*a(n-13) +22*a(n-14) -60*a(n-15) -144*a(n-16) +42*a(n-17) -254*a(n-18) -28*a(n-19) -120*a(n-20) -72*a(n-21) +36*a(n-22) -4*a(n-23) +12*a(n-24) for n>27

A224157 Number of nX7 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

29, 267, 1252, 4339, 13283, 39037, 114537, 340134, 1025559, 3143071, 9794989, 31018972, 99708260, 324764638, 1069736878, 3556096357, 11908005965, 40101772888, 135631552056, 460218357877, 1565350043268, 5333698073679

Offset: 1

R. H. Hardin Mar 31 2013

nonn

Column 7 of A224158

			Some solutions for n=3
..1..0..0..0..0..0..0....0..0..0..0..0..0..0....0..0..0..0..0..1..1
..0..1..0..0..0..0..0....0..0..0..0..0..1..0....0..0..0..1..1..1..1
..1..1..1..1..0..0..0....1..1..1..1..1..0..0....0..0..1..1..1..1..1

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

Empirical: a(n) = 8*a(n-1) -20*a(n-2) +11*a(n-3) +13*a(n-4) +18*a(n-5) -83*a(n-6) +98*a(n-7) -99*a(n-8) +159*a(n-9) -264*a(n-10) +312*a(n-11) -324*a(n-12) +647*a(n-13) -757*a(n-14) +88*a(n-15) +283*a(n-16) -257*a(n-17) -451*a(n-18) +365*a(n-19) -1074*a(n-20) +477*a(n-21) -1092*a(n-22) +258*a(n-23) -916*a(n-24) -142*a(n-25) +114*a(n-26) +202*a(n-27) +118*a(n-28) -56*a(n-29) +56*a(n-30) -24*a(n-31) +8*a(n-32) -8*a(n-33) for n>37

A224159 Number of 3 X n 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

8, 36, 89, 187, 373, 702, 1252, 2130, 3479, 5486, 8391, 12497, 18181, 25906, 36234, 49840, 67527, 90242, 119093, 155367, 200549, 256342, 324688, 407790, 508135, 628518, 772067, 942269, 1142997, 1378538, 1653622, 1973452, 2343735, 2770714

Offset: 1

R. H. Hardin, Mar 31 2013

nonn

Row 3 of A224158.

			Some solutions for n=3:
..0..0..1....0..0..1....0..0..0....0..1..0....1..0..0....0..1..1....1..1..0
..1..1..0....1..1..0....0..0..0....1..0..0....0..1..0....1..1..1....1..0..0
..1..1..1....1..1..0....1..0..0....0..1..0....1..0..0....1..1..0....1..1..0

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

Cf. A224158.

Empirical: a(n) = (1/720)*n^6 + (1/240)*n^5 + (47/144)*n^4 - (3/16)*n^3 + (1111/180)*n^2 - (199/60)*n + 20 for n>2.
Conjectures from Colin Barker, Aug 28 2018: (Start)
G.f.: x*(8 - 20*x + 5*x^2 + 40*x^3 - 47*x^4 - 5*x^5 + 41*x^6 - 27*x^7 + 6*x^8) / (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>9.
(End)

A224160 Number of 4 X n 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

16, 108, 281, 574, 1156, 2271, 4339, 8008, 14257, 24519, 40840, 66082, 104179, 160456, 242022, 358249, 521350, 747070, 1055505, 1472065, 2028598, 2764693, 3729181, 4981854, 6595423, 8657737, 11274286, 14571012, 18697453, 23830246

Offset: 1

R. H. Hardin, Mar 31 2013

nonn

Row 4 of A224158.

			Some solutions for n=3:
..1..1..0....1..1..0....1..1..0....0..0..0....1..1..1....0..0..1....0..0..1
..1..1..0....1..1..1....1..1..1....0..0..0....1..1..1....0..1..0....0..1..1
..1..1..0....1..1..1....1..1..0....1..1..0....1..1..1....1..1..1....1..1..0
..1..0..0....1..1..0....1..1..0....1..1..1....1..1..0....1..1..1....1..1..0

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

Cf. A224158.

Empirical: a(n) = (1/40320)*n^8 - (1/10080)*n^7 + (31/2880)*n^6 + (43/720)*n^5 + (3527/5760)*n^4 - (5947/1440)*n^3 + (548119/10080)*n^2 - (119221/840)*n + 283 for n>4.
Conjectures from Colin Barker, Aug 28 2018: (Start)
G.f.: x*(16 - 36*x - 115*x^2 + 589*x^3 - 950*x^4 + 519*x^5 + 442*x^6 - 977*x^7 + 817*x^8 - 436*x^9 + 178*x^10 - 55*x^11 + 9*x^12) / (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>13.
(End)

A224161 Number of 5Xn 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

32, 324, 900, 1783, 3469, 6786, 13283, 25624, 48339, 88755, 158358, 274636, 463580, 763045, 1227226, 1932567, 2985495, 4532457, 6772837, 9975443, 14499382, 20820285, 29563005, 41542090, 57811531, 79725503, 109012056, 147861974

Offset: 1

R. H. Hardin Mar 31 2013

nonn

Row 5 of A224158

			Some solutions for n=3
..0..0..0....0..1..0....0..0..0....1..1..0....0..1..1....0..0..1....0..1..0
..0..0..0....1..0..0....0..0..1....1..0..0....1..1..0....0..1..0....1..0..0
..1..1..0....0..0..0....1..1..0....0..0..0....1..1..0....1..0..0....0..1..1
..1..1..1....1..0..0....1..0..0....0..1..0....1..0..0....0..1..0....1..1..0
..1..1..1....1..0..0....1..0..0....1..1..1....1..0..0....1..1..0....1..0..0

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

Empirical: a(n) = (1/3628800)*n^10 - (1/241920)*n^9 + (13/60480)*n^8 - (1/2688)*n^7 + (15793/172800)*n^6 - (10013/11520)*n^5 + (3158927/362880)*n^4 - (461413/12096)*n^3 + (13189843/50400)*n^2 - (797567/840)*n + 2301 for n>6

A224162 Number of 6Xn 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

64, 972, 2935, 5657, 10562, 20065, 39037, 76393, 148637, 284937, 535211, 981957, 1757541, 3068802, 5231637, 8719051, 14227266, 22765909, 35780116, 55314683, 84233265, 126509183, 187608775, 274993564, 398773975, 572555093, 814524213

Offset: 1

R. H. Hardin Mar 31 2013

nonn

Row 6 of A224158

			Some solutions for n=3
..0..0..1....1..1..0....0..0..1....0..0..1....1..0..0....1..0..0....0..0..0
..0..1..0....1..0..0....1..1..0....0..1..0....0..0..0....0..1..0....1..0..0
..1..0..0....1..0..0....1..0..0....1..0..0....0..0..0....1..0..0....0..0..1
..0..1..1....1..1..0....1..0..0....1..1..1....0..1..0....1..1..0....0..1..0
..1..1..1....1..1..0....0..0..0....1..1..1....1..1..0....1..1..1....1..0..0
..1..1..1....1..1..1....0..1..0....1..1..1....1..0..0....1..1..0....1..1..0

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

Empirical: a(n) = (1/479001600)*n^12 - (1/15966720)*n^11 + (127/43545600)*n^10 - (7/207360)*n^9 + (4033/2073600)*n^8 - (5443/483840)*n^7 + (13552621/43545600)*n^6 - (8448991/1451520)*n^5 + (1032695879/10886400)*n^4 - (8305531/10368)*n^3 + (67691137/14850)*n^2 - (80407927/5544)*n + 24225 for n>8

cp's OEIS Frontend

A224152 Number of n X n 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

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A224153 Number of n X 3 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

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A224154 Number of nX4 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

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A224155 Number of nX5 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

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A224156 Number of nX6 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

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A224157 Number of nX7 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

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A224159 Number of 3 X n 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

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A224160 Number of 4 X n 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

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A224161 Number of 5Xn 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

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A224162 Number of 6Xn 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

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