A001611 -id:A001611 - cp's OEIS frontend

A157728 a(n) = Fibonacci(n) - 4.

1, 4, 9, 17, 30, 51, 85, 140, 229, 373, 606, 983, 1593, 2580, 4177, 6761, 10942, 17707, 28653, 46364, 75021, 121389, 196414, 317807, 514225, 832036, 1346265, 2178305, 3524574, 5702883, 9227461, 14930348, 24157813, 39088165, 63245982, 102334151

Offset: 5

N. J. A. Sloane, Jun 26 2010

Partial sums of A071679. - R. J. Mathar, Oct 12 2010

Vincenzo Librandi, Table of n, a(n) for n = 5..287
Paul Barry, The Triple Riordan Group, arXiv:2412.05461 [math.CO], 2024. See pp. 5, 10.
Index entries for linear recurrences with constant coefficients, signature (2,0,-1).

Cf. A000045, A001611, A000071, A157725, A001911, A157726, A006327, A157727, A157728, A157729, A167616.

a157728 = subtract 4 . a000045  -- Reinhard Zumkeller, Oct 31 2013

[ Fibonacci(n) - 4: n in [5..50] ]; // Vincenzo Librandi, Apr 24 2011

Fibonacci[Range[5,40]]-4 (* or *) LinearRecurrence[{2,0,-1},{1,4,9},40] (* Harvey P. Dale, Jan 17 2022 *)

a(n)=fibonacci(n) - 4 \\ Charles R Greathouse IV, Jun 11 2015

From R. J. Mathar, Oct 12 2010: (Start)
a(n) = 2*a(n-1) - a(n-3).
G.f.: x^5*(1+x)^2/((x-1)*(x^2+x-1)). (End)

A157729 a(n) = Fibonacci(n) + 5.

Original entry on oeis.org

5, 6, 6, 7, 8, 10, 13, 18, 26, 39, 60, 94, 149, 238, 382, 615, 992, 1602, 2589, 4186, 6770, 10951, 17716, 28662, 46373, 75030, 121398, 196423, 317816, 514234, 832045, 1346274, 2178314, 3524583, 5702892, 9227470, 14930357, 24157822, 39088174, 63245991, 102334160

Offset: 0

N. J. A. Sloane, Jun 26 2010

Vincenzo Librandi, Table of n, a(n) for n = 0..285
Ivana Jovović and Branko Malešević, Some enumerations of non-trivial composition of the differential operations and the directional derivative, Notes on Number Theory and Discrete Mathematics, Vol. 23, 2017, No. 1, 28-38.
Index entries for linear recurrences with constant coefficients, signature (2,0,-1).

Cf. A000045, A001611, A000071, A157725, A001911, A157726, A006327, A157727, A157728, A157729, A167616.

a157729 = (+ 5) . a000045
a157729_list = 5 : 6 : map (subtract 5)
                       (zipWith (+) a157729_list $ tail a157729_list)
-- Reinhard Zumkeller, Jul 30 2013

[ Fibonacci(n) + 5: n in [0..40] ]; // Vincenzo Librandi, Apr 24 2011

Fibonacci[Range[0,40]]+5 (* or *) LinearRecurrence[{2,0,-1},{5,6,6},50] (* Harvey P. Dale, Aug 17 2012 *)

a(n)=fibonacci(n)+5 \\ Charles R Greathouse IV, Jul 02 2013

G.f.: ( 5-4*x-6*x^2 ) / ( (x-1)*(x^2+x-1) ). - R. J. Mathar, Aug 09 2012
a(0)=5, a(1)=6, a(2)=6, a(n)=2*a(n-1)+0*a(n-2)-a(n-3). - Harvey P. Dale, Aug 17 2012
a(0) = 5, a(1) = 6, a(n) = a(n - 2) + a(n - 1) - 5. - Reinhard Zumkeller, Jul 30 2013

A207717 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 0 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 10, 36, 36, 9, 16, 100, 114, 81, 14, 26, 256, 450, 387, 196, 22, 42, 676, 1644, 2205, 1414, 484, 35, 68, 1764, 6186, 12015, 11970, 5302, 1225, 56, 110, 4624, 23010, 66339, 97580, 66946, 20265, 3136, 90, 178, 12100, 85992, 364869, 805154

Offset: 1

R. H. Hardin Feb 19 2012

Table starts
..2....4.....6......10.......16.........26..........42............68
..4...16....36.....100......256........676........1764..........4624
..6...36...114.....450.....1644.......6186.......23010.........85992
..9...81...387....2205....12015......66339......364869.......2009223
.14..196..1414...11970....97580.....805154.....6614706......54438356
.22..484..5302...66946...820820...10150118...125165018....1545006848
.35.1225.20265..383845..7070805..131365535..2433018665...45118588165
.56.3136.78120.2221688.61530000.1717508184.47808913432.1332236625328

			Some solutions for n=4 k=3
..1..1..1....1..1..1....1..0..1....0..1..0....1..0..0....1..0..1....1..0..1
..1..1..1....0..1..1....1..1..1....0..1..1....0..1..1....0..1..1....0..1..0
..1..1..1....1..1..1....0..1..0....0..1..1....1..1..0....1..0..0....1..1..1
..1..1..0....0..1..1....1..0..1....0..1..0....1..1..1....1..1..1....1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..763

Column 1 is A001611(n+2)
Column 2 is A207436
Row 1 is A006355(n+2)
Row 2 is A206981

A240783 T(n,k)=Number of nXk 0..1 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..1 introduced in row major order.

Original entry on oeis.org

1, 1, 2, 1, 3, 4, 1, 4, 11, 8, 1, 6, 20, 34, 16, 1, 9, 46, 97, 111, 32, 1, 14, 97, 305, 459, 361, 64, 1, 22, 216, 959, 2167, 2187, 1172, 128, 1, 35, 472, 3033, 10150, 15332, 10442, 3809, 256, 1, 56, 1043, 9581, 47920, 106411, 108509, 49861, 12377, 512, 1, 90, 2296, 30354

Offset: 1

R. H. Hardin, Apr 12 2014

Table starts
...1.....1.......1........1..........1...........1.............1..............1
...2.....3.......4........6..........9..........14............22.............35
...4....11......20.......46.........97.........216...........472...........1043
...8....34......97......305........959........3033..........9581..........30354
..16...111.....459.....2167......10150.......47920........226532........1071982
..32...361....2187....15332.....106411......746346.......5228820.......36701371
..64..1172...10442...108509....1120383....11677893.....121621207.....1269199948
.128..3809...49861...767834...11791412...182610635....2827515311....43857418181
.256.12377..238068..5434887..124095989..2856212777...65742420202..1515928067679
.512.40218.1136678.38467875.1306056075.44672652785.1528546759636.52397680462958

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

R. H. Hardin, Table of n, a(n) for n = 1..264

Column 1 is A000079(n-1)
Column 2 is A180762
Row 2 is A001611(n+1)

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)
k=3: a(n) = 5*a(n-1) -a(n-2) -a(n-3) +4*a(n-4) -4*a(n-5) -3*a(n-6) +a(n-7)
k=4: [order 22]
k=5: [order 54]
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: a(n) = 2*a(n-1) -a(n-3)
n=3: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -a(n-5)
n=4: [order 15]
n=5: [order 30] for n>34
n=6: [order 94]

A302515 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 3, 3, 4, 5, 3, 4, 8, 8, 5, 11, 6, 16, 13, 7, 15, 9, 9, 32, 21, 13, 21, 28, 14, 14, 64, 34, 23, 52, 36, 48, 21, 22, 128, 55, 37, 118, 80, 90, 89, 28, 35, 256, 89, 63, 220, 235, 199, 184, 163, 37, 56, 512, 144, 109, 408, 541, 689, 458, 376, 297, 51, 90, 1024, 233, 183

Offset: 1

R. H. Hardin, Apr 09 2018

Table starts
...1..2..3...5....8...13....21.....34......55......89......144.......233
...2..3..3...5....7...13....23.....37......63.....109......183.......309
...4..4.11..15...21...52...118....220.....408.....852.....1764......3460
...8..6..9..28...36...80...235....541....1115....2554.....6095.....13920
..16..9.14..48...90..199...689...2125....5410...13908....39850....114503
..32.14.21..89..184..458..1784...7182...22544...67096...220654....775150
..64.22.28.163..376.1088..4558..23944...95681..344525..1302832...5550086
.128.35.37.297..832.2651.12324..82857..414880.1775176..7735877..39371229
.256.56.51.544.1744.6257.32336.282857.1748514.8778929.44362463.272701915

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

R. H. Hardin, Table of n, a(n) for n = 1..511

Column 1 is A000079(n-1).
Column 2 is A001611(n+1).
Row 1 is A000045(n+1).
Row 2 is A003227(n-1) for n>2.

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) -a(n-3)
k=3: a(n) = a(n-1) +a(n-4) for n>7
k=4: a(n) = a(n-1) +2*a(n-3) +2*a(n-4) -a(n-6) -a(n-7) for n>10
k=5: a(n) = a(n-1) +6*a(n-3) +2*a(n-5) -12*a(n-6) -4*a(n-7) +8*a(n-9) for n>11
k=6: a(n) = a(n-1) +6*a(n-3) +5*a(n-4) +3*a(n-5) -8*a(n-6) -6*a(n-7) -3*a(n-8) for n>12
k=7: [order 15] for n>21
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = a(n-1) +2*a(n-3) for n>5
n=3: a(n) = a(n-1) +2*a(n-3) +4*a(n-4) for n>7
n=4: a(n) = a(n-1) +a(n-2) +3*a(n-3) +5*a(n-4) -a(n-5) -5*a(n-6) -4*a(n-7) for n>10
n=5: [order 13] for n>17
n=6: [order 23] for n>29
n=7: [order 50] for n>55

A302680 T(n,k)=Number of nXk 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

1, 2, 2, 3, 3, 4, 5, 3, 4, 8, 8, 5, 8, 6, 16, 13, 7, 12, 7, 9, 32, 21, 13, 18, 20, 11, 14, 64, 34, 23, 40, 30, 33, 18, 22, 128, 55, 37, 94, 76, 63, 64, 29, 35, 256, 89, 63, 184, 217, 187, 125, 121, 47, 56, 512, 144, 109, 358, 509, 661, 453, 257, 231, 76, 90, 1024, 233, 183, 760

Offset: 1

R. H. Hardin, Apr 11 2018

Table starts
...1..2..3...5....8...13....21.....34......55.......89......144.......233
...2..3..3...5....7...13....23.....37......63......109......183.......309
...4..4..8..12...18...40....94....184.....358......760.....1594......3220
...8..6..7..20...30...76...217....509....1189.....3034.....7569.....18274
..16..9.11..33...63..187...661...1837....5075....15661....46975....135191
..32.14.18..64..125..453..2013...6725...21745....80985...295335...1015113
..64.22.29.121..257.1125..6311..25139...96728...439233..1942666...8017639
.128.35.47.231..528.2782.19497..92889..422915..2330640.12480973..61679118
.256.56.76.440.1085.6843.60253.343421.1847358.12346637.80210343.474618407

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

R. H. Hardin, Table of n, a(n) for n = 1..799

Column 1 is A000079(n-1).
Column 2 is A001611(n+1).
Row 1 is A000045(n+1).
Row 2 is A003229(n-1) for n>2.

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) -a(n-3)
k=3: a(n) = a(n-1) +a(n-2) for n>5
k=4: a(n) = a(n-1) +2*a(n-2) -a(n-4) for n>8
k=5: a(n) = a(n-1) +3*a(n-3) +2*a(n-4) +2*a(n-5) for n>10
k=6: 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
k=7: [order 12] for n>19
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = a(n-1) +2*a(n-3) for n>5
n=3: a(n) = a(n-1) +3*a(n-3) +3*a(n-4) for n>7
n=4: 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
n=5: [order 11] for n>16
n=6: [order 17] for n>23
n=7: [order 31] for n>38

A303314 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 3, 3, 4, 5, 3, 4, 8, 8, 5, 12, 6, 16, 13, 7, 17, 11, 9, 32, 21, 13, 24, 36, 19, 14, 64, 34, 23, 67, 50, 74, 34, 22, 128, 55, 37, 158, 128, 139, 165, 53, 35, 256, 89, 63, 298, 439, 410, 349, 361, 83, 56, 512, 144, 109, 595, 1085, 1799, 1221, 853, 783, 136, 90, 1024, 233

Offset: 1

R. H. Hardin, Apr 21 2018

Table starts
...1..2...3....5....8....13.....21......34.......55........89........144
...2..3...3....5....7....13.....23......37.......63.......109........183
...4..4..12...17...24....67....158.....298......595......1337.......2863
...8..6..11...36...50...128....439....1085.....2431......6452......17455
..16..9..19...74..139...410...1799....5907....16494.....53290.....184915
..32.14..34..165..349..1221...7096...30280...102683....403872....1783894
..64.22..53..361..853..3453..26184..148313...618149...2955145...16591424
.128.35..83..783.2180.10223.100128..746323..3851318..22515378..159560449
.256.56.136.1710.5525.30247.387892.3784002.23967605.171306353.1539204838

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

R. H. Hardin, Table of n, a(n) for n = 1..511

Column 1 is A000079(n-1).
Column 2 is A001611(n+1).
Row 1 is A000045(n+1).
Row 2 is A003229(n-1) for n>2.

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) -a(n-3)
k=3: a(n) = a(n-1) +a(n-3) +a(n-4) for n>7
k=4: a(n) = a(n-1) +a(n-2) +3*a(n-3) +2*a(n-4) -a(n-5) -2*a(n-6) -a(n-7) for n>10
k=5: a(n) = a(n-1) +9*a(n-3) +2*a(n-4) +4*a(n-5) -10*a(n-6) -6*a(n-7) +4*a(n-9) for n>12
k=6: [order 8] for n>11
k=7: [order 20] for n>23
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = a(n-1) +2*a(n-3) for n>5
n=3: a(n) = a(n-1) +3*a(n-3) +4*a(n-4) for n>7
n=4: a(n) = a(n-1) +a(n-2) +5*a(n-3) +9*a(n-4) -3*a(n-5) -7*a(n-6) -2*a(n-7) for n>11
n=5: [order 12] for n>16
n=6: [order 23] for n>28
n=7: [order 46] for n>51

A207488 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 1 1 and 1 1 0 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 9, 13, 81, 82, 81, 14, 18, 169, 217, 177, 196, 22, 25, 324, 499, 530, 408, 484, 35, 34, 625, 1014, 1322, 1459, 942, 1225, 56, 46, 1156, 2141, 2749, 4041, 3947, 2233, 3136, 90, 62, 2116, 4188, 6217, 8808, 12151, 11306, 5348, 8100, 145, 83

Offset: 1

R. H. Hardin Feb 18 2012

Table starts
..2....4....6.....9.....13.....18.....25......34......46.......62.......83
..4...16...36....81....169....324....625....1156....2116.....3844.....6889
..6...36...82...217....499...1014...2141....4188....8150....15670....29517
..9...81..177...530...1322...2749...6217...12712...25908....52474...103704
.14..196..408..1459...4041...8808..21991...48044..105558...230156...490287
.22..484..942..3947..12151..26980..73325..170276..397692...935992..2150515
.35.1225.2233.11306..39050..89417.268275..667760.1691526..4324858.10910668
.56.3136.5348.32445.126411.292136.959855.2555724.6929562.19404152.53733153

			Some solutions for n=4 k=3
..1..1..1....0..1..0....0..0..1....1..0..1....0..1..0....0..0..1....0..1..0
..1..1..1....0..0..1....0..0..1....1..0..1....1..1..0....0..1..0....0..0..1
..1..1..1....1..1..0....1..0..1....1..0..1....0..1..0....0..0..1....1..0..0
..1..1..1....0..0..1....0..0..1....1..0..1....1..1..1....0..1..0....0..0..1

R. H. Hardin, Table of n, a(n) for n = 1..577

Column 1 is A001611(n+2)
Column 2 is A207436
Row 1 is A171861(n+1)
Row 2 is A207025
Row 3 is A207270

A207500 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 0 0 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 9, 13, 81, 102, 81, 14, 18, 169, 283, 297, 196, 22, 25, 324, 699, 1004, 932, 484, 35, 34, 625, 1526, 2942, 3939, 2974, 1225, 56, 46, 1156, 3355, 7305, 14253, 15495, 9723, 3136, 90, 62, 2116, 6888, 17911, 41938, 68745, 62530, 32164

Offset: 1

R. H. Hardin Feb 18 2012

Table starts
..2....4.....6......9......13......18.......25........34........46.........62
..4...16....36.....81.....169.....324......625......1156......2116.......3844
..6...36...102....283.....699....1526.....3355......6888.....13954......27816
..9...81...297...1004....2942....7305....17911.....40262.....87990.....187012
.14..196...932...3939...14253...41938...122061....319798....813724....2009628
.22..484..2974..15495...68745..237576...804887...2408502...6896518...18962878
.35.1225..9723..62530..343310.1413961..5715255..20090516..67370124..216796950
.56.3136.32164.253747.1714707.8384076.40046975.163471950.628620128.2300337450

			Some solutions for n=4 k=3
..1..0..0....1..0..0....1..1..1....0..1..0....0..1..0....0..1..0....0..0..1
..0..0..1....1..0..1....1..1..1....0..1..0....0..0..1....1..1..0....1..1..1
..1..0..0....1..0..0....1..1..1....0..1..0....0..1..0....1..1..0....0..0..1
..1..0..1....0..0..1....1..1..1....0..1..0....0..0..1....1..0..0....1..1..0

R. H. Hardin, Table of n, a(n) for n = 1..390

Column 1 is A001611(n+2)
Column 2 is A207436
Row 1 is A171861(n+1)
Row 2 is A207025
Row 3 is A207243

A207564 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 1 1 and 1 1 0 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 9, 14, 81, 92, 81, 14, 21, 196, 241, 221, 196, 22, 31, 441, 720, 636, 618, 484, 35, 46, 961, 1889, 2234, 2135, 1690, 1225, 56, 68, 2116, 4719, 6315, 9568, 6709, 4861, 3136, 90, 100, 4624, 12102, 16812, 32823, 36426, 23276, 13900

Offset: 1

R. H. Hardin Feb 18 2012

Table starts
..2....4.....6.....9.....14......21.......31........46........68........100
..4...16....36....81....196.....441......961......2116......4624......10000
..6...36....92...241....720....1889.....4719.....12102.....30414......74588
..9...81...221...636...2234....6315....16812.....47596....129150.....337186
.14..196...618..2135...9568...32823...106833....378104...1270366....4115246
.22..484..1690..6709..36426..138017...493471...1980774...7259428...25276248
.35.1225..4861.23276.160652..738515..3275898..16648464..77299468..346860730
.56.3136.13900.78733.666212.3451393.17232331.100565794.513390118.2498101416

			Some solutions for n=4 k=3
..1..0..1....1..0..1....1..1..0....1..0..0....0..1..1....1..1..1....0..0..0
..1..0..1....0..1..1....0..0..0....0..0..0....1..1..1....1..1..1....1..1..1
..1..0..1....1..0..1....1..0..1....1..0..1....0..1..1....1..1..1....0..0..0
..1..1..1....0..1..1....0..0..0....0..0..0....1..1..1....1..1..1....0..0..0

R. H. Hardin, Table of n, a(n) for n = 1..511

Column 1 is A001611(n+2)
Column 2 is A207436
Row 1 is A038718(n+2)
Row 2 is A207069
Row 3 is A207414

cp's OEIS Frontend

A157728 a(n) = Fibonacci(n) - 4.

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A157729 a(n) = Fibonacci(n) + 5.

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A207717 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 0 vertically.

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A240783 T(n,k)=Number of nXk 0..1 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..1 introduced in row major order.

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A302515 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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A302680 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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A303314 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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A207488 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 1 1 and 1 1 0 vertically.

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A207500 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 0 0 vertically.

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