A281765 -id:A281765 - cp's OEIS frontend

A281760 Number of n X 3 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

2, 14, 47, 90, 201, 374, 672, 1172, 2015, 3442, 5859, 9952, 16876, 28574, 48309, 81554, 137477, 231418, 389016, 653080, 1095019, 1833842, 3067719, 5126372, 8557988, 14273314, 23784417, 39600082, 65880265, 109518782, 181933584, 302025692

Offset: 1

R. H. Hardin, Jan 29 2017

nonn

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

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

Column 3 of A281765.

Empirical: a(n) = 4*a(n-1) - 4*a(n-2) - 2*a(n-3) + 4*a(n-4) - a(n-6) for n>11.

Empirical g.f.: x*(2 + 6*x - x^2 - 38*x^3 + 49*x^4 - 32*x^5 - 26*x^6 + 36*x^7 + 6*x^8 + 8*x^9 + 8*x^10) / ((1 - x)^2*(1 - x - x^2)^2). - Colin Barker, Feb 20 2019

A281761 Number of nX4 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

2, 40, 152, 560, 1872, 5948, 18358, 55048, 162120, 471340, 1355236, 3862260, 10924470, 30702868, 85814996, 238711156, 661252798, 1824976204, 5020176620, 13769014596, 37664818800, 102784444960, 279880084494, 760592396664

Offset: 1

R. H. Hardin, Jan 29 2017

nonn

Column 4 of A281765.

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

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

Cf. A281765.

Empirical: a(n) = 7*a(n-1) -13*a(n-2) -5*a(n-3) +19*a(n-4) +21*a(n-5) +3*a(n-6) -63*a(n-7) -59*a(n-8) +83*a(n-9) +140*a(n-10) -186*a(n-11) -149*a(n-12) +197*a(n-13) +248*a(n-14) +70*a(n-15) -370*a(n-16) -268*a(n-17) +503*a(n-18) +307*a(n-19) -822*a(n-20) -226*a(n-21) +724*a(n-22) -54*a(n-23) -310*a(n-24) +156*a(n-25) +80*a(n-26) -44*a(n-27) +3*a(n-28) +9*a(n-29) for n>32

A281762 Number of nX5 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

5, 110, 609, 2808, 12191, 49986, 201450, 795220, 3098932, 11944444, 45648773, 173194466, 653072024, 2449607050, 9146028282, 34010834368, 126024445869, 465494253234, 1714507604630, 6298717534388, 23086454425976, 84439440608072

Offset: 1

R. H. Hardin, Jan 29 2017

nonn

Column 5 of A281765.

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

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

Cf. A281765.

Empirical: a(n) = 10*a(n-1) -29*a(n-2) +2*a(n-3) +52*a(n-4) +170*a(n-5) -239*a(n-6) -674*a(n-7) +73*a(n-8) +1874*a(n-9) +1456*a(n-10) -3556*a(n-11) -2269*a(n-12) +228*a(n-13) +7955*a(n-14) -1394*a(n-15) -5270*a(n-16) -4208*a(n-17) -6664*a(n-18) +6626*a(n-19) +10430*a(n-20) +21576*a(n-21) -48939*a(n-22) +56684*a(n-23) -32865*a(n-24) +17584*a(n-25) +71780*a(n-26) -98666*a(n-27) +76825*a(n-28) -82636*a(n-29) -20094*a(n-30) -4536*a(n-31) -85926*a(n-32) -352*a(n-33) -69440*a(n-34) -14036*a(n-35) -30493*a(n-36) -20432*a(n-37) -9763*a(n-38) -14256*a(n-39) -787*a(n-40) -5248*a(n-41) -1167*a(n-42) -738*a(n-43) -218*a(n-44) +76*a(n-45) -209*a(n-46) +120*a(n-47) -16*a(n-48) for n>57

A281763 Number of nX6 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

8, 280, 2138, 13968, 85844, 502276, 2848436, 15817652, 86332266, 465260812, 2481799950, 13127073212, 68942510184, 359901720360, 1869047959784, 9662464139924, 49753587454582, 255286283139832, 1305758265647346

Offset: 1

R. H. Hardin, Jan 29 2017

nonn

Column 6 of A281765.

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

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

Cf. A281765.

A281764 Number of nX7 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

15, 698, 7466, 68362, 589990, 4845178, 38998648, 306847534, 2376142873, 18172170592, 137541600309, 1032205229342, 7690612680576, 56948407735784, 419460675116112, 3075312381551048, 22455267348093278, 163373533509709066

Offset: 1

R. H. Hardin, Jan 29 2017

nonn

Column 7 of A281765.

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

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

Cf. A281765.

A281766 Number of 2 X n 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

0, 4, 14, 40, 110, 280, 698, 1696, 4052, 9564, 22330, 51728, 118998, 272228, 619804, 1405456, 3175966, 7155320, 16078698, 36048008, 80656900, 180149700, 401740002, 894646944, 1989842814, 4420825196, 9811946668, 21757950712, 48209235558

Offset: 1

R. H. Hardin, Jan 29 2017

nonn

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

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

Row 2 of A281765.

Empirical: a(n) = 4*a(n-1) + a(n-2) - 16*a(n-3) - a(n-4) + 30*a(n-5) + 4*a(n-6) - 24*a(n-7) - 4*a(n-8) + 8*a(n-9).

Empirical g.f.: 2*x^2*(1 - x)*(1 + x)*(2 - x - 8*x^2 - x^3 + 6*x^4) / ((1 - 2*x)*(1 - x - 3*x^2 + 2*x^4)^2). - Colin Barker, Feb 20 2019

A281767 Number of 3Xn 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

0, 10, 47, 152, 609, 2138, 7466, 25798, 87397, 293470, 979311, 3235714, 10650401, 34842532, 113507950, 368400482, 1191351902, 3841448788, 12352142633, 39620840414, 126807886700, 405026431154, 1291283976919, 4109819232304

Offset: 1

R. H. Hardin, Jan 29 2017

nonn

Row 3 of A281765.

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

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

Cf. A281765.

Empirical: a(n) = 6*a(n-1) +7*a(n-2) -80*a(n-3) -60*a(n-4) +610*a(n-5) +488*a(n-6) -2954*a(n-7) -2778*a(n-8) +9782*a(n-9) +10423*a(n-10) -24116*a(n-11) -27411*a(n-12) +46820*a(n-13) +54750*a(n-14) -74006*a(n-15) -87429*a(n-16) +97522*a(n-17) +114272*a(n-18) -108436*a(n-19) -124098*a(n-20) +102206*a(n-21) +112813*a(n-22) -81722*a(n-23) -85782*a(n-24) +55064*a(n-25) +54233*a(n-26) -30842*a(n-27) -28193*a(n-28) +14078*a(n-29) +11842*a(n-30) -5088*a(n-31) -3915*a(n-32) +1398*a(n-33) +977*a(n-34) -274*a(n-35) -172*a(n-36) +34*a(n-37) +19*a(n-38) -2*a(n-39) -a(n-40) for n>41

A281768 Number of 4Xn 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

0, 20, 90, 560, 2808, 13968, 68362, 323280, 1529974, 7114300, 32915192, 151142772, 689726508, 3133687480, 14169310798, 63838844556, 286639424578, 1283124275056, 5728711606322, 25513799290264, 113382456085042, 502859346935932

Offset: 1

R. H. Hardin, Jan 29 2017

nonn

Row 4 of A281765.

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

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

Cf. A281765.

A281769 Number of 5Xn 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

0, 38, 201, 1872, 12191, 85844, 589990, 3845590, 25703392, 166880128, 1080273873, 6965900750, 44487321221, 283503705456, 1797488483677, 11352536170284, 71500155029453, 448832589255878, 2810514285498993, 17557109431928644

Offset: 1

R. H. Hardin, Jan 29 2017

nonn

Row 5 of A281765.

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

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

Cf. A281765.

A281770 Number of 6Xn 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

0, 68, 374, 5948, 49986, 502276, 4845178, 43943360, 414035752, 3763905492, 34161108524, 309491219676, 2770210355448, 24781891977992, 220487430433918, 1953506661837984, 17268182347051482, 152093095781502104

Offset: 1

R. H. Hardin, Jan 29 2017

nonn

Row 6 of A281765.

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

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

Cf. A281765.

cp's OEIS Frontend

A281760 Number of n X 3 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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A281761 Number of nX4 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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A281762 Number of nX5 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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A281763 Number of nX6 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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A281764 Number of nX7 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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A281766 Number of 2 X n 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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A281767 Number of 3Xn 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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A281768 Number of 4Xn 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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A281769 Number of 5Xn 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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A281770 Number of 6Xn 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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