A279977 -id:A279977 - cp's OEIS frontend

A279971 Number of n X 2 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

1, 3, 9, 31, 108, 366, 1205, 3873, 12207, 37859, 115842, 350412, 1049545, 3116655, 9185349, 26890375, 78253896, 226510362, 652483133, 1871302893, 5345409483, 15213423371, 43153001406, 122024489304, 344061371665, 967537410459

Offset: 1

R. H. Hardin, Dec 24 2016

nonn

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

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

Column 2 of A279977.

Empirical: a(n) = 9*a(n-1) - 30*a(n-2) + 45*a(n-3) - 30*a(n-4) + 9*a(n-5) -a(n-6).

Empirical g.f.: x*(1 - 2*x)*(1 - 4*x + 4*x^2 + 3*x^3) / (1 - 3*x + x^2)^3. - Colin Barker, Feb 12 2019

A279972 Number of n X 3 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

0, 9, 50, 296, 1650, 8666, 43543, 211650, 1002602, 4652327, 21225237, 95473540, 424318824, 1866436977, 8136431834, 35191126234, 151149336828, 645183934470, 2738696392197, 11567109056460, 48632928912442, 203627897130121

Offset: 1

R. H. Hardin, Dec 24 2016

nonn

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

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

Column 3 of A279977.

Empirical: a(n) = 15*a(n-1) - 90*a(n-2) + 281*a(n-3) - 510*a(n-4) + 585*a(n-5) - 437*a(n-6) + 210*a(n-7) - 60*a(n-8) + 8*a(n-9) for n>10.

Empirical g.f.: x^2*(9 - 85*x + 356*x^2 - 819*x^3 + 1096*x^4 - 888*x^5 + 438*x^6 - 124*x^7 + 16*x^8) / (1 - 5*x + 5*x^2 - 2*x^3)^3. - Colin Barker, Feb 12 2019

A279973 Number of nX4 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

3, 24, 221, 1922, 15511, 118857, 876704, 6281773, 43997218, 302544617, 2049122034, 13702872583, 90643155972, 593994248709, 3860755349595, 24913212937078, 159737403339158, 1018352525988640, 6458838814490585, 40774568909571868

Offset: 1

R. H. Hardin, Dec 24 2016

nonn

Column 4 of A279977.

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

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

Cf. A279977.

Empirical: a(n) = 30*a(n-1) -399*a(n-2) +3163*a(n-3) -17061*a(n-4) +67920*a(n-5) -210660*a(n-6) +527724*a(n-7) -1093560*a(n-8) +1904479*a(n-9) -2816082*a(n-10) +3556545*a(n-11) -3846177*a(n-12) +3560349*a(n-13) -2812614*a(n-14) +1885732*a(n-15) -1064382*a(n-16) +500283*a(n-17) -192971*a(n-18) +59883*a(n-19) -14538*a(n-20) +2649*a(n-21) -339*a(n-22) +27*a(n-23) -a(n-24)

A279974 Number of nX5 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

3, 62, 822, 10491, 124030, 1393359, 15071233, 158391708, 1627160233, 16409869901, 162982613326, 1598047779214, 15497697410287, 148874926975376, 1418326347449973, 13414045478319926, 126045765506261814

Offset: 1

R. H. Hardin, Dec 24 2016

nonn

Column 5 of A279977.

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

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

Cf. A279977.

Empirical: a(n) = 53*a(n-1) -1291*a(n-2) +19418*a(n-3) -204835*a(n-4) +1632329*a(n-5) -10324115*a(n-6) +53654890*a(n-7) -234937934*a(n-8) +882771616*a(n-9) -2885212091*a(n-10) +8285140483*a(n-11) -21058509124*a(n-12) +47630930849*a(n-13) -96230469370*a(n-14) +174085724937*a(n-15) -282388861308*a(n-16) +410961960219*a(n-17) -536498538568*a(n-18) +627876381653*a(n-19) -658110830698*a(n-20) +617080503289*a(n-21) -516968320637*a(n-22) +386461849324*a(n-23) -257438979196*a(n-24) +152574757688*a(n-25) -80292463252*a(n-26) +37420429652*a(n-27) -15389322205*a(n-28) +5557085609*a(n-29) -1749901992*a(n-30) +476005587*a(n-31) -110393019*a(n-32) +21427460*a(n-33) -3388972*a(n-34) +419408*a(n-35) -38032*a(n-36) +2240*a(n-37) -64*a(n-38) for n>39

A279975 Number of nX6 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

9, 134, 2669, 50690, 887491, 14787217, 237386464, 3703836674, 56499013470, 846166990079, 12481300976351, 181756380764316, 2617908346883386, 37350611059955815, 528493982152145690, 7423498639698400616

Offset: 1

R. H. Hardin, Dec 24 2016

nonn

Column 6 of A279977.

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

R. H. Hardin, Table of n, a(n) for n = 1..202
R. H. Hardin, Empirical recurrence of order 96

Cf. A279977.

Empirical recurrence of order 96 (see link above)

A279976 Number of n X 7 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

15, 277, 8068, 226771, 5870751, 144819856, 3444870482, 79672440007, 1801951754910, 40020022178950, 875485447655303, 18909516686710743, 403990472666974061, 8549840572786983933, 179455644823143101693

Offset: 1

R. H. Hardin, Dec 24 2016

nonn

Column 7 of A279977.

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

R. H. Hardin, Table of n, a(n) for n = 1..82

Cf. A279977.

A279978 Number of 2 X n 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

0, 3, 9, 24, 62, 134, 277, 542, 1035, 1930, 3546, 6432, 11555, 20590, 36445, 64140, 112326, 195866, 340241, 589038, 1016671, 1749950, 3004610, 5147092, 8798911, 15012766, 25569393, 43477440, 73814414, 125140142, 211870477, 358260350

Offset: 1

R. H. Hardin, Dec 24 2016

nonn

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

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

Row 2 of A279977.

Empirical: a(n) = 5*a(n-1) - 7*a(n-2) - 2*a(n-3) + 10*a(n-4) - 2*a(n-5) - 5*a(n-6) + a(n-7) + a(n-8) for n>10.

Empirical g.f.: x^2*(3 - 6*x + 11*x^3 - 20*x^4 + 5*x^5 + 12*x^6 + 2*x^7 - 5*x^8) / ((1 - x)^2*(1 - x - x^2)^3). - Colin Barker, Feb 12 2019

A279979 Number of 3 X n 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

0, 9, 50, 221, 822, 2669, 8068, 23169, 64250, 173509, 459148, 1195219, 3069280, 7791834, 19587853, 48827241, 120818815, 297018329, 725970958, 1765237102, 4272245780, 10296018246, 24717636634, 59130589267, 140997069400, 335205034089, 794714054209, 1879307452216

Offset: 1

R. H. Hardin, Dec 24 2016

nonn

Row 3 of A279977.

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

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

Cf. A279977.

Empirical: a(n) = 9*a(n-1) -33*a(n-2) +60*a(n-3) -36*a(n-4) -78*a(n-5) +199*a(n-6) -165*a(n-7) -33*a(n-8) +200*a(n-9) -180*a(n-10) +66*a(n-11) +22*a(n-12) -78*a(n-13) +84*a(n-14) -40*a(n-15) -21*a(n-16) +15*a(n-17) -3*a(n-18) +18*a(n-19) +6*a(n-20) -4*a(n-21) -3*a(n-22) -3*a(n-23) -a(n-24) for n>30.

A279980 Number of 4Xn 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

0, 31, 296, 1922, 10491, 50690, 226771, 963728, 3941732, 15655280, 60749739, 231325874, 867192006, 3208394065, 11737643962, 42526452550, 152777627539, 544782076812, 1929805835927, 6795769111934, 23804414728200, 82983605105905

Offset: 1

R. H. Hardin, Dec 24 2016

nonn

Row 4 of A279977.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 68

Cf. A279977.

Empirical recurrence of order 68 (see link above)

A279981 Number of 5Xn 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

0, 108, 1650, 15511, 124030, 887491, 5870751, 37029063, 224989656, 1329149598, 7678897522, 43562801122, 243417797716, 1342868232191, 7327618165054, 39607933952548, 212329659406086, 1129989079237450, 5974847669219636

Offset: 1

R. H. Hardin, Dec 24 2016

nonn

Row 5 of A279977.

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

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

Cf. A279977.

cp's OEIS Frontend

A279971 Number of n X 2 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A279972 Number of n X 3 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A279973 Number of nX4 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A279974 Number of nX5 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A279975 Number of nX6 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A279976 Number of n X 7 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A279978 Number of 2 X n 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A279979 Number of 3 X n 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A279980 Number of 4Xn 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A279981 Number of 5Xn 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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