A297682 -id:A297682 - cp's OEIS frontend

A297677 Number of n X 3 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 1 or 4 neighboring 1's.

7, 29, 150, 742, 3744, 18840, 94891, 477850, 2406649, 12120617, 61043229, 307433020, 1548331209, 7797889752, 39272660089, 197789648884, 996131790595, 5016837561113, 25266394843590, 127249627060291, 640869727748787

Offset: 1

R. H. Hardin, Jan 03 2018

nonn

Column 3 of A297682.

			Some solutions for n=7
..1..0..1. .0..1..0. .0..0..0. .0..0..1. .1..0..1. .0..1..0. .1..0..1
..1..0..0. .1..0..0. .0..0..1. .0..0..1. .1..0..0. .1..0..0. .1..0..0
..1..0..0. .0..0..1. .0..0..1. .0..1..0. .0..0..0. .0..0..0. .1..1..1
..0..1..0. .0..0..0. .1..0..0. .0..1..0. .0..0..1. .1..1..0. .1..0..0
..0..0..0. .0..0..1. .1..0..0. .0..0..1. .1..0..1. .0..0..0. .1..0..1
..0..1..0. .0..0..0. .1..0..0. .0..0..0. .0..1..0. .1..0..1. .0..0..0
..0..1..0. .0..0..1. .0..0..1. .1..1..0. .1..0..1. .0..0..0. .0..1..1

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

Cf. A297682.

Empirical: a(n) = 5*a(n-1) -a(n-2) +8*a(n-3) -5*a(n-4) -30*a(n-5) +17*a(n-6).

A297678 Number of nX4 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 1 or 4 neighboring 1s.

Original entry on oeis.org

13, 80, 629, 4633, 34872, 260924, 1955750, 14651847, 109783269, 822547725, 6162992737, 46176452589, 345979170190, 2592263829464, 19422650189445, 145525052534819, 1090352803546358, 8169515919608631, 61210454258421286

Offset: 1

R. H. Hardin, Jan 03 2018

nonn

Column 4 of A297682.

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

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

Cf. A297682.

Empirical: a(n) = 6*a(n-1) +10*a(n-2) +6*a(n-3) +26*a(n-4) -31*a(n-5) -a(n-6) -165*a(n-7) -22*a(n-8) +181*a(n-9) +39*a(n-10) -54*a(n-11) -15*a(n-12) +6*a(n-13) -4*a(n-14) -a(n-15) +2*a(n-16)

A297679 Number of nX5 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 1 or 4 neighboring 1s.

Original entry on oeis.org

24, 219, 2790, 32911, 401678, 4870764, 59210634, 719647644, 8748946600, 106360216813, 1293051641215, 15720067945295, 191114672847915, 2323452694839402, 28247100678589725, 343410814460992551

Offset: 1

R. H. Hardin, Jan 03 2018

nonn

Column 5 of A297682.

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

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

Cf. A297682.

Empirical: a(n) = 13*a(n-1) -13*a(n-2) +103*a(n-3) -631*a(n-4) -2904*a(n-5) +4228*a(n-6) -9174*a(n-7) +33373*a(n-8) -11504*a(n-9) +48969*a(n-10) -94831*a(n-11) +2069*a(n-12) -31085*a(n-13) -9102*a(n-14) +78809*a(n-15) -13808*a(n-16) +49758*a(n-17) -54323*a(n-18) +6349*a(n-19) +12263*a(n-20) -9120*a(n-21) +1613*a(n-22) -13130*a(n-23) +13637*a(n-24) -72*a(n-25) -8310*a(n-26) +1120*a(n-27) +2320*a(n-28) +128*a(n-29) -192*a(n-30)

A297680 Number of nX6 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 1 or 4 neighboring 1s.

Original entry on oeis.org

44, 597, 12110, 221420, 4202440, 78957968, 1487819051, 28013761161, 527589764007, 9935480401770, 187107516285853, 3523634803856570, 66357694370878682, 1249658843756374555, 23533781410865979450

Offset: 1

R. H. Hardin, Jan 03 2018

nonn

Column 6 of A297682.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 57

Cf. A297682.

Empirical recurrence of order 57 (see link above)

A297681 Number of nX7 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 1 or 4 neighboring 1s.

Original entry on oeis.org

81, 1632, 52889, 1519630, 45865837, 1368968852, 41030621948, 1229127412701, 36837288191422, 1103993847036050, 33088254114520559, 991712287397354032, 29723613829882860702, 890879134522839275761, 26701570968782131551720

Offset: 1

R. H. Hardin, Jan 03 2018

nonn

Column 7 of A297682.

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

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

Cf. A297682.

A297683 Number of 3Xn 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 1 or 4 neighboring 1s.

Original entry on oeis.org

8, 33, 150, 629, 2790, 12110, 52889, 230406, 1005170, 4382278, 19110183, 83327912, 363357551, 1584416863, 6908888883, 30126285845, 131366174343, 572824066436, 2497808102429, 10891729292407, 47493549245614, 207096331298600

Offset: 1

R. H. Hardin, Jan 03 2018

nonn

Row 3 of A297682.

			Some solutions for n=7
..0..1..0..0..0..0..1. .0..0..0..1..0..0..0. .0..0..1..0..0..0..1
..1..0..0..0..0..1..1. .0..0..0..1..0..0..0. .1..0..0..0..0..0..0
..0..0..0..0..1..0..1. .0..0..0..0..1..0..1. .1..0..1..1..0..0..1

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

Cf. A297682.

Empirical: a(n) = 2*a(n-1) +7*a(n-2) +11*a(n-3) +17*a(n-4) -7*a(n-5) -10*a(n-6) -18*a(n-7) -a(n-8)

A297684 Number of 4Xn 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 1 or 4 neighboring 1s.

Original entry on oeis.org

16, 98, 742, 4633, 32911, 221420, 1519630, 10322924, 70546581, 480682141, 3279483836, 22360879158, 152513668108, 1040062673807, 7093214269529, 48373908268204, 329903456068580, 2249876994245104, 15343785763900111

Offset: 1

R. H. Hardin, Jan 03 2018

nonn

Row 4 of A297682.

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

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

Cf. A297682.

Empirical: a(n) = 2*a(n-1) +20*a(n-2) +60*a(n-3) +184*a(n-4) +57*a(n-5) -73*a(n-6) -458*a(n-7) +105*a(n-8) +215*a(n-9) +380*a(n-10) -574*a(n-11) -435*a(n-12) +162*a(n-13) -270*a(n-14) -87*a(n-15) +32*a(n-16) +8*a(n-17)

A297685 Number of 5Xn 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 1 or 4 neighboring 1s.

Original entry on oeis.org

32, 291, 3744, 34872, 401678, 4202440, 45865837, 488402012, 5277134441, 56590184544, 609118876500, 6543424122789, 70369098323857, 756319883731372, 8131309593772974, 87407051279518533, 939657110269352989

Offset: 1

R. H. Hardin, Jan 03 2018

nonn

Row 5 of A297682.

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

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

Cf. A297682.

Empirical: a(n) = 4*a(n-1) +45*a(n-2) +198*a(n-3) +1120*a(n-4) -571*a(n-5) +949*a(n-6) -25951*a(n-7) +43907*a(n-8) -121981*a(n-9) +237707*a(n-10) -305033*a(n-11) +951497*a(n-12) -2179565*a(n-13) +1393985*a(n-14) +38155*a(n-15) +856624*a(n-16) +1417955*a(n-17) -2925138*a(n-18) +4386425*a(n-19) -3349236*a(n-20) +7904975*a(n-21) -936917*a(n-22) +6331851*a(n-23) -431305*a(n-24) -2123285*a(n-25) -1887476*a(n-26) -6000225*a(n-27) -5171754*a(n-28) -5025966*a(n-29) -3580724*a(n-30) +728778*a(n-31) +1200558*a(n-32) +668712*a(n-33) +511075*a(n-34) +1377776*a(n-35) +458144*a(n-36) +151448*a(n-37) -54584*a(n-38) -42912*a(n-39) -30464*a(n-40) +3840*a(n-41)

A297686 Number of 6Xn 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 1 or 4 neighboring 1s.

Original entry on oeis.org

64, 865, 18840, 260924, 4870764, 78957968, 1368968852, 22772982621, 388437292266, 6536987996149, 110788354031138, 1870242391300687, 31643467601797592, 534716690271693434, 9041935800076605287

Offset: 1

R. H. Hardin, Jan 03 2018

nonn

Row 6 of A297682.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
Robert Israel, Linear recurrence of order 102
Robert Israel, Maple-assisted proof of recurrence

Cf. A297682.

Linear recurrence of order 102 (see links). - Robert Israel, Oct 28 2019

A297687 Number of 7Xn 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 1 or 4 neighboring 1s.

Original entry on oeis.org

128, 2570, 94891, 1955750, 59210634, 1487819051, 41030621948, 1066508741933, 28748828127508, 759564088991329, 20288126990340123, 538493726660721622, 14345913847238205189, 381379710626740656598, 10150876741291095683850

Offset: 1

R. H. Hardin, Jan 03 2018

nonn

Row 7 of A297682.

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

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

Cf. A297682.

cp's OEIS Frontend

A297677 Number of n X 3 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 1 or 4 neighboring 1's.

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A297678 Number of nX4 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 1 or 4 neighboring 1s.

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A297679 Number of nX5 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 1 or 4 neighboring 1s.

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A297680 Number of nX6 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 1 or 4 neighboring 1s.

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A297681 Number of nX7 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 1 or 4 neighboring 1s.

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A297683 Number of 3Xn 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 1 or 4 neighboring 1s.

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A297684 Number of 4Xn 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 1 or 4 neighboring 1s.

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A297685 Number of 5Xn 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 1 or 4 neighboring 1s.

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A297686 Number of 6Xn 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 1 or 4 neighboring 1s.

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