A297506 -id:A297506 - cp's OEIS frontend

A297501 Number of nX3 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 2 neighboring 1s.

4, 31, 110, 531, 2534, 11405, 53175, 246040, 1135117, 5253716, 24286811, 112274796, 519155469, 2400230989, 11097385328, 51309028043, 237225520918, 1096808926323, 5071081279846, 23446053720513, 108402467083427, 501197081280420

Offset: 1

R. H. Hardin, Dec 31 2017

nonn

Column 3 of A297506.

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

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

Cf. A297506.

Empirical: a(n) = a(n-1) +5*a(n-2) +37*a(n-3) +63*a(n-4) +101*a(n-5) -45*a(n-6) -198*a(n-7) -254*a(n-8) -40*a(n-9) +88*a(n-10) +96*a(n-11)

A297502 Number of nX4 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 2 neighboring 1s.

Original entry on oeis.org

7, 68, 314, 2281, 14201, 88808, 573119, 3613793, 22999331, 146183595, 928047561, 5898371728, 37468267405, 238038322708, 1512327060362, 9607753234896, 61039432234655, 387788945511548, 2463656446529920, 15651856594703719

Offset: 1

R. H. Hardin, Dec 31 2017

nonn

Column 4 of A297506.

			Some solutions for n=6
..1..1..1..0. .1..1..1..0. .0..1..0..0. .0..1..1..0. .0..1..0..0
..0..1..0..0. .0..0..0..1. .1..1..0..0. .0..0..0..0. .1..0..0..1
..0..1..0..1. .1..1..0..0. .1..0..0..1. .0..1..0..0. .0..0..1..0
..1..0..1..0. .0..0..1..0. .0..0..1..0. .0..1..1..0. .0..0..0..1
..0..0..0..0. .0..0..1..0. .1..0..0..0. .0..0..1..0. .0..1..1..0
..1..1..0..0. .1..1..0..0. .1..1..0..0. .1..1..0..0. .0..0..1..0

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

Cf. A297506.

Empirical: a(n) = 2*a(n-1) +19*a(n-2) +58*a(n-3) -7*a(n-4) -41*a(n-5) -196*a(n-6) -202*a(n-7) -78*a(n-8) +196*a(n-9) +176*a(n-10) +122*a(n-11) +19*a(n-12) +37*a(n-13) +22*a(n-14) +21*a(n-15) +10*a(n-16) -a(n-17) -a(n-18)

A297503 Number of n X 5 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 2 neighboring 1's.

Original entry on oeis.org

12, 218, 1829, 23348, 270845, 3075264, 35919085, 414559944, 4794512057, 55494787360, 641788518693, 7424878808114, 85894097165753, 993622743583263, 11494556544048474, 132971604823085666, 1538246171030926340

Offset: 1

R. H. Hardin, Dec 31 2017

nonn

Column 5 of A297506.

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

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

Cf. A297506.

Empirical: a(n) = 3*a(n-1) +40*a(n-2) +458*a(n-3) +2079*a(n-4) +7392*a(n-5) -5377*a(n-6) -86832*a(n-7) -163832*a(n-8) +108859*a(n-9) +615980*a(n-10) -108605*a(n-11) -1854189*a(n-12) +509278*a(n-13) +13561851*a(n-14) +28930737*a(n-15) +17333565*a(n-16) -58819317*a(n-17) -189849419*a(n-18) -179930295*a(n-19) +95206355*a(n-20) +312188246*a(n-21) +206553457*a(n-22) +45142449*a(n-23) -114274549*a(n-24) -80784244*a(n-25) -20472387*a(n-26) +50954802*a(n-27) +22152613*a(n-28) +10927600*a(n-29) +4324241*a(n-30) +3214027*a(n-31) +2536913*a(n-32) +4108007*a(n-33) -2976528*a(n-34) -2837327*a(n-35) -788083*a(n-36) +28130*a(n-37) -27293*a(n-38) -77317*a(n-39) -57585*a(n-40) -27063*a(n-41) -4725*a(n-42) +4025*a(n-43) +4394*a(n-44) +955*a(n-45) -271*a(n-46) -10*a(n-47) -37*a(n-48) +12*a(n-49) -a(n-50).

A297504 Number of nX6 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 2 neighboring 1s.

Original entry on oeis.org

21, 729, 8803, 191192, 3624914, 66289769, 1272836591, 23896899569, 450529429259, 8509989217247, 160423654526876, 3026744089971807, 57099188342748031, 1077069529621543033, 20318551052028606846, 383290619891741250595

Offset: 1

R. H. Hardin, Dec 31 2017

nonn

Column 6 of A297506.

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

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

Cf. A297506.

A297505 Number of nX7 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 2 neighboring 1s.

Original entry on oeis.org

37, 2097, 34757, 1247716, 35049871, 978288822, 28914051279, 823340493402, 23748019543354, 684563956136832, 19685697905900807, 567106229569054219, 16326031115140984900, 470031756510991757935, 13533758185630160222532

Offset: 1

R. H. Hardin, Dec 31 2017

nonn

Column 7 of A297506.

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

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

Cf. A297506.

A297507 Number of 2 X n 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 2 neighboring 1s.

Original entry on oeis.org

1, 10, 31, 68, 218, 729, 2097, 6139, 18932, 57273, 170792, 514608, 1554993, 4677797, 14071941, 42401182, 127713015, 384477424, 1157762858, 3486768241, 10499588277, 31616525407, 95208917296, 286707283257, 863361068252, 2599853035248

Offset: 1

R. H. Hardin, Dec 31 2017

nonn

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

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

Row 2 of A297506.

Empirical: a(n) = 3*a(n-1) - 2*a(n-2) + 9*a(n-3) - 6*a(n-4) - 8*a(n-5).

Empirical g.f.: x*(1 + 7*x + 3*x^2 - 14*x^3 - 8*x^4) / (1 - 3*x + 2*x^2 - 9*x^3 + 6*x^4 + 8*x^5). - Colin Barker, Feb 28 2019

A297508 Number of 3 X n 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 2 neighboring 1s.

Original entry on oeis.org

1, 29, 110, 314, 1829, 8803, 34757, 157673, 735144, 3208028, 14196017, 64154943, 286007061, 1271032033, 5685858000, 25403326244, 113255416409, 505585282497, 2257780807909, 10075966019543, 44971626813134, 200763429520862

Offset: 1

R. H. Hardin, Dec 31 2017

nonn

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

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

Row 3 of A297506.

Empirical: a(n) = 3*a(n-1) + a(n-2) + 32*a(n-3) - 15*a(n-4) - 65*a(n-5) - 74*a(n-6) + 56*a(n-7) + 24*a(n-8) - 3*a(n-9) + 12*a(n-10).

Empirical g.f.: x*(1 + 26*x + 22*x^2 - 77*x^3 - 136*x^4 - 18*x^5 + 80*x^6 + 21*x^7 + 9*x^8 + 12*x^9) / (1 - 3*x - x^2 - 32*x^3 + 15*x^4 + 65*x^5 + 74*x^6 - 56*x^7 - 24*x^8 + 3*x^9 - 12*x^10). - Colin Barker, Feb 28 2019

A297509 Number of 4Xn 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 2 neighboring 1s.

Original entry on oeis.org

1, 87, 531, 2281, 23348, 191192, 1247716, 9450219, 74086027, 542295341, 4014135733, 30366147431, 226985241429, 1690164545942, 12658565659102, 94748613114792, 707806468257951, 5292426347783239, 39588593164337549

Offset: 1

R. H. Hardin, Dec 31 2017

nonn

Row 4 of A297506.

			Some solutions for n=6
..1..1..0..0..1..0. .0..0..0..0..0..1. .1..1..1..1..0..0. .0..0..0..0..0..1
..0..0..0..1..1..0. .0..0..0..0..1..0. .0..0..0..0..0..0. .0..1..1..0..1..0
..0..0..0..0..0..1. .0..0..0..0..1..0. .0..0..0..1..0..0. .0..0..0..0..0..0
..0..1..1..0..1..0. .0..0..0..1..0..1. .0..1..1..0..1..0. .0..1..1..0..1..1

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

Cf. A297506.

Empirical: a(n) = 6*a(n-1) +a(n-2) +122*a(n-3) -209*a(n-4) -1087*a(n-5) -354*a(n-6) +4059*a(n-7) +1206*a(n-8) +3818*a(n-9) +692*a(n-10) -11767*a(n-11) -6075*a(n-12) -2835*a(n-13) -949*a(n-14) +8451*a(n-15) +6295*a(n-16) -636*a(n-17) +2500*a(n-18) -3242*a(n-19) -1428*a(n-20) +742*a(n-21) +74*a(n-22) -24*a(n-23) +2*a(n-24)

A297510 Number of 5Xn 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 2 neighboring 1s.

Original entry on oeis.org

1, 280, 2534, 14201, 270845, 3624914, 35049871, 431068698, 5534003000, 63359116756, 744028146659, 9066464960896, 107792105015031, 1274517673890830, 15252160661225132, 182090112172787219, 2165329133215506254

Offset: 1

R. H. Hardin, Dec 31 2017

nonn

Row 5 of A297506.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 59

Cf. A297506.

Empirical recurrence of order 59 (see link above)

A297511 Number of 6Xn 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 2 neighboring 1s.

Original entry on oeis.org

1, 876, 11405, 88808, 3075264, 66289769, 978288822, 19677228473, 410226893539, 7428573953424, 139931054756836, 2750243232989133, 52290968094715743, 990034495588191380, 19031260437956001426, 364274317770524751427

Offset: 1

R. H. Hardin, Dec 31 2017

nonn

Row 6 of A297506.

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

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

Cf. A297506.

cp's OEIS Frontend

A297501 Number of nX3 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 2 neighboring 1s.

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A297502 Number of nX4 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 2 neighboring 1s.

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A297503 Number of n X 5 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 2 neighboring 1's.

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A297504 Number of nX6 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 2 neighboring 1s.

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A297505 Number of nX7 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 2 neighboring 1s.

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A297507 Number of 2 X n 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 2 neighboring 1s.

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A297508 Number of 3 X n 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 2 neighboring 1s.

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A297509 Number of 4Xn 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 2 neighboring 1s.

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A297510 Number of 5Xn 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 2 neighboring 1s.

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A297511 Number of 6Xn 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 2 neighboring 1s.

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