A283572 -id:A283572 - cp's OEIS frontend

A283567 Number of nX3 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.

1, 26, 169, 1108, 6453, 36038, 194173, 1021432, 5275885, 26869458, 135310457, 675163708, 3343196861, 16447661790, 80470971869, 391822686752, 1899839181365, 9177752354378, 44190339947417, 212148874972196, 1015791721800101

Offset: 1

R. H. Hardin, Mar 11 2017

nonn

Column 3 of A283572.

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

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

Cf. A283572.

Empirical: a(n) = 10*a(n-1) -27*a(n-2) -4*a(n-3) +89*a(n-4) -106*a(n-5) -85*a(n-6) +228*a(n-7) -60*a(n-8) -192*a(n-9) +144*a(n-10) +64*a(n-11) -64*a(n-12)

A283568 Number of nX4 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.

Original entry on oeis.org

2, 72, 674, 6812, 60802, 528436, 4441052, 36589848, 296555892, 2373574616, 18804085974, 147722885964, 1152326125736, 8934988081564, 68923216977218, 529275667161388, 4048382091614590, 30857555674174468, 234469910144650842

Offset: 1

R. H. Hardin, Mar 11 2017

nonn

Column 4 of A283572.

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

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

Cf. A283572.

Empirical: a(n) = 12*a(n-1) -16*a(n-2) -148*a(n-3) +122*a(n-4) +8*a(n-5) -1218*a(n-6) +1236*a(n-7) +1851*a(n-8) -3776*a(n-9) +3314*a(n-10) +5408*a(n-11) -7569*a(n-12) -2532*a(n-13) +2620*a(n-14) +320*a(n-15) -256*a(n-16)

A283569 Number of nX5 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.

Original entry on oeis.org

5, 282, 4313, 67892, 945100, 12699250, 164714523, 2089140956, 26034179747, 320066184088, 3892257109768, 46912556808052, 561231923565665, 6671995763846662, 78889299491699749, 928412437363667396

Offset: 1

R. H. Hardin, Mar 11 2017

nonn

Column 5 of A283572.

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

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

Cf. A283572.

Empirical: a(n) = 26*a(n-1) -199*a(n-2) +132*a(n-3) +4265*a(n-4) -17778*a(n-5) -15431*a(n-6) +219544*a(n-7) -281138*a(n-8) -1030440*a(n-9) +2246322*a(n-10) +1755192*a(n-11) -1811285*a(n-12) -3285434*a(n-13) -13913513*a(n-14) +16913132*a(n-15) +1232775*a(n-16) +17203018*a(n-17) -24077179*a(n-18) -4811576*a(n-19) +3633696*a(n-20) +13901264*a(n-21) +3953216*a(n-22) -16310568*a(n-23) -2421451*a(n-24) +6596550*a(n-25) +5162315*a(n-26) -3560308*a(n-27) -4199693*a(n-28) +2503442*a(n-29) +1473667*a(n-30) -1059728*a(n-31) -255854*a(n-32) +261176*a(n-33) +18126*a(n-34) -39936*a(n-35) +1121*a(n-36) +3850*a(n-37) -347*a(n-38) -220*a(n-39) +29*a(n-40) +6*a(n-41) -a(n-42)

A283570 Number of nX6 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.

Original entry on oeis.org

12, 908, 21186, 509952, 10919674, 226897932, 4558585174, 89724600000, 1736716820366, 33188681249924, 627668838247742, 11769603893466432, 219120313902873796, 4054721455598417092, 74638990577755174088

Offset: 1

R. H. Hardin, Mar 11 2017

nonn

Column 6 of A283572.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 54

Cf. A283572.

Empirical recurrence of order 54 (see link above)

A283571 Number of nX7 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.

Original entry on oeis.org

26, 2832, 104464, 3890056, 129527524, 4173039716, 129997769458, 3965206666608, 118919078661476, 3520469545329364, 103128721861954074, 2995091644500263428, 86357662212925835570, 2474720063522591410712, 70543862532039328231208

Offset: 1

R. H. Hardin, Mar 11 2017

nonn

Column 7 of A283572.

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

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

Cf. A283572.

A283573 Number of 2Xn 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.

Original entry on oeis.org

0, 4, 26, 72, 282, 908, 2832, 8856, 26750, 80088, 237190, 695272, 2024064, 5853676, 16835874, 48194664, 137385394, 390201476, 1104636144, 3118021376, 8778028806, 24653647608, 69091665822, 193246772832, 539525988960, 1503796131028

Offset: 1

R. H. Hardin, Mar 11 2017

nonn

Row 2 of A283572.

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

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

Cf. A283572.

Empirical: a(n) = 2*a(n-1) +5*a(n-2) +2*a(n-3) -17*a(n-4) -24*a(n-5) -16*a(n-6).

Empirical: G.f.: 2*x^2*(2+9*x)/(-1+x+3*x^2+4*x^3)^2 . - R. J. Mathar, Mar 11 2017

A283574 Number of 3Xn 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.

Original entry on oeis.org

0, 16, 169, 674, 4313, 21186, 104464, 513458, 2431143, 11478378, 53471911, 246887096, 1132514276, 5160569268, 23395062541, 105570183858, 474452680669, 2124725208078, 9484785230640, 42219767106150, 187451695326747

Offset: 1

R. H. Hardin, Mar 11 2017

nonn

Row 3 of A283572.

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

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

Cf. A283572.

Empirical: a(n) = 4*a(n-1) +10*a(n-2) -6*a(n-3) -105*a(n-4) -108*a(n-5) -85*a(n-6) -14*a(n-7) -250*a(n-8) +176*a(n-9) -145*a(n-10) +44*a(n-11) -4*a(n-12)

A283575 Number of 4Xn 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.

Original entry on oeis.org

0, 68, 1108, 6812, 67892, 509952, 3890056, 29428836, 214600036, 1561753984, 11203805186, 79697223948, 563151495500, 3952776211644, 27603742610922, 191869394908352, 1328251534591608, 9162408587486912, 63001467075539154

Offset: 1

R. H. Hardin, Mar 11 2017

nonn

Row 4 of A283572.

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

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

Cf. A283572.

Empirical: a(n) = 4*a(n-1) +34*a(n-2) +48*a(n-3) -561*a(n-4) -2288*a(n-5) -5234*a(n-6) -5692*a(n-7) -8384*a(n-8) +4044*a(n-9) -3814*a(n-10) +27880*a(n-11) -6865*a(n-12) +31280*a(n-13) -24250*a(n-14) +14500*a(n-15) -21025*a(n-16)

A283576 Number of 5Xn 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.

Original entry on oeis.org

0, 256, 6453, 60802, 945100, 10919674, 129527524, 1518039552, 17162725531, 193879598458, 2157351957174, 23818259818860, 261203745411854, 2845597456824844, 30846423421417897, 332823725660697214

Offset: 1

R. H. Hardin, Mar 11 2017

nonn

Row 5 of A283572.

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

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

Cf. A283572.

Empirical: a(n) = 8*a(n-1) +68*a(n-2) +60*a(n-3) -3476*a(n-4) -14270*a(n-5) -44938*a(n-6) -22046*a(n-7) -330622*a(n-8) +510556*a(n-9) -2390879*a(n-10) +12030076*a(n-11) -33356941*a(n-12) +109298060*a(n-13) -275521313*a(n-14) +720665120*a(n-15) -1806543117*a(n-16) +3736469200*a(n-17) -6762740424*a(n-18) +9106885902*a(n-19) -8972101747*a(n-20) +5725392444*a(n-21) +1465366745*a(n-22) -4653650006*a(n-23) +5324165465*a(n-24) -6499265632*a(n-25) -1325270370*a(n-26) +4246454996*a(n-27) -6037898483*a(n-28) +4489487644*a(n-29) +550019212*a(n-30) +225055032*a(n-31) +2503394292*a(n-32) -1535246836*a(n-33) -69578999*a(n-34) +500958770*a(n-35) -1021093565*a(n-36) -36310362*a(n-37) +1083010*a(n-38) +1959144*a(n-39) +32639*a(n-40) -1740*a(n-41) -900*a(n-42)

A283577 Number of 6Xn 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.

Original entry on oeis.org

0, 924, 36038, 528436, 12699250, 226897932, 4173039716, 75680334636, 1325245534158, 23188665136084, 399584953679136, 6833558444087984, 116073651385176490, 1958677669677212976, 32888238393714753228

Offset: 1

R. H. Hardin, Mar 11 2017

nonn

Row 6 of A283572.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 64

Cf. A283572.

Empirical recurrence of order 64 (see link above)

cp's OEIS Frontend

A283567 Number of nX3 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.

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A283568 Number of nX4 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.

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A283569 Number of nX5 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.

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A283570 Number of nX6 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.

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A283571 Number of nX7 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.

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A283573 Number of 2Xn 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.

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A283574 Number of 3Xn 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.

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A283575 Number of 4Xn 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.

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A283576 Number of 5Xn 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.

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