A275228 -id:A275228 - cp's OEIS frontend

A275222 Number of n X 2 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,0) and new values introduced in order 0..2.

2, 6, 11, 27, 66, 162, 404, 1007, 2512, 6271, 15655, 39084, 97580, 243626, 608259, 1518638, 3791579, 9466427, 23634810, 59008986, 147327628, 367832623, 918367048, 2292885359, 5724642759, 14292705300, 35684571668, 89093606034, 222439846275

Offset: 1

R. H. Hardin, Jul 20 2016

nonn

			Some solutions for n=4:
..0..1. .0..0. .0..1. .0..1. .0..1. .0..1. .0..0. .0..1. .0..1. .0..1
..1..0. .1..2. .1..0. .1..0. .2..0. .1..0. .1..2. .1..2. .1..0. .2..0
..2..2. .2..1. .0..2. .2..1. .0..2. .0..1. .2..1. .2..1. .0..2. .0..1
..1..0. .1..2. .2..0. .1..2. .1..1. .1..2. .0..0. .1..2. .1..0. .2..0

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

Column 2 of A275228.

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

Empirical g.f.: x*(1 + x - x^2)*(2 - 2*x - x^2 - x^3) / ((1 - x)*(1 - 2*x - x^2 - x^3 + x^4)). - Colin Barker, Feb 01 2019

A275223 Number of nX3 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

5, 36, 61, 187, 648, 2282, 8134, 29027, 103456, 368889, 1315431, 4690476, 16725240, 59638892, 212660009, 758302172, 2703951339, 9641739667, 34380480348, 122593793026, 437144505226, 1558768299519, 5558250385696, 19819589184889

Offset: 1

R. H. Hardin, Jul 20 2016

nonn

Column 3 of A275228.

			Some solutions for n=4
..0..0..1. .0..1..0. .0..1..1. .0..1..2. .0..0..1. .0..1..1. .0..1..2
..2..1..2. .2..2..1. .2..0..2. .1..2..1. .1..1..2. .2..0..2. .2..0..1
..1..2..1. .0..1..0. .0..2..0. .0..1..0. .2..2..1. .0..2..0. .0..1..2
..2..1..0. .1..0..1. .1..0..1. .1..2..1. .0..0..2. .2..0..2. .1..0..1

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

Cf. A275228.

Empirical: a(n) = 3*a(n-1) +5*a(n-2) -10*a(n-3) -a(n-4) -10*a(n-5) +21*a(n-6) -4*a(n-7) -4*a(n-8) +a(n-9) for n>13

A275224 Number of nX4 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

14, 216, 339, 1302, 6448, 32388, 164645, 844176, 4319300, 22083548, 112975642, 578036947, 2957212295, 15128798774, 77399122215, 395975649916, 2025811842566, 10364054079218, 53022552043867, 271263640161978, 1387785882638203

Offset: 1

R. H. Hardin, Jul 20 2016

nonn

Column 4 of A275228.

			Some solutions for n=4
..0..1..2..0. .0..1..2..0. .0..1..0..1. .0..0..0..0. .0..1..0..2
..1..2..0..1. .1..0..1..2. .1..0..1..0. .1..2..1..1. .1..0..2..0
..0..1..2..0. .0..1..2..0. .0..2..0..1. .2..1..2..2. .2..2..0..1
..1..2..0..1. .1..0..1..2. .2..0..1..0. .1..0..0..0. .1..0..1..0

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

Cf. A275228.

Empirical: a(n) = 6*a(n-1) -4*a(n-2) +18*a(n-4) -213*a(n-5) +254*a(n-6) -43*a(n-7) +348*a(n-8) +571*a(n-9) -1746*a(n-10) -33*a(n-11) +741*a(n-12) -1412*a(n-13) +2606*a(n-14) -243*a(n-15) -667*a(n-16) +1424*a(n-17) -2763*a(n-18) +1382*a(n-19) -742*a(n-20) +329*a(n-21) +281*a(n-22) -97*a(n-23) +88*a(n-24) -62*a(n-25) -27*a(n-26) -3*a(n-27) +7*a(n-28) -a(n-29) +3*a(n-30) -a(n-31) for n>35

A275225 Number of nX5 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

41, 1296, 1885, 9075, 64248, 460034, 3334854, 24595019, 181187962, 1332436071, 9810172225, 72273272964, 532374394904, 3921375107766, 28886433275447, 212793855415512, 1567545471803795, 11547327991701749, 85063839496736654

Offset: 1

R. H. Hardin, Jul 20 2016

nonn

Column 5 of A275228.

			Some solutions for n=4
..0..1..0..1..0. .0..1..0..1..0. .0..1..2..1..0. .0..0..0..1..0
..2..0..1..2..2. .1..0..2..2..1. .1..0..1..0..1. .2..1..1..2..1
..0..2..2..1..0. .0..2..0..1..2. .0..1..0..1..0. .1..2..2..1..2
..2..0..1..0..1. .2..0..1..0..0. .1..2..1..2..2. .0..0..0..0..1

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 81

Cf. A275228.

Empirical recurrence of order 81 (see link above)

A275226 Number of nX6 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

122, 7776, 10483, 63267, 640250, 6534900, 67550874, 716735348, 7605814181, 80496567059, 853665236582, 9065417241908, 96259306327146, 1022092822313136, 10854887473630824, 115290893519800111, 1224514266243749236

Offset: 1

R. H. Hardin, Jul 20 2016

nonn

Column 6 of A275228.

			Some solutions for n=4
..0..1..2..1..2..1. .0..1..2..0..0..0. .0..1..2..1..1..1. .0..1..2..1..0..1
..1..2..1..2..1..2. .2..2..1..2..1..2. .1..2..1..2..0..0. .1..2..1..2..1..0
..2..1..0..1..0..0. .0..1..2..1..2..1. .2..1..2..0..2..2. .2..1..2..1..2..2
..1..2..1..2..1..2. .1..0..0..2..1..2. .1..2..1..2..1..1. .0..0..1..2..1..0

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

Cf. A275228.

A275227 Number of nX7 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

365, 46656, 58301, 441090, 6380362, 92831330, 1368326231, 20887845278, 319348056936, 4865299894416, 74341935372850, 1138486477148165, 17435551839365877, 267037909717137282, 4091456524318196661

Offset: 1

R. H. Hardin, Jul 20 2016

nonn

Column 7 of A275228.

			Some solutions for n=3
..0..1..0..1..2..2..0. .0..0..0..0..0..0..0. .0..1..0..1..0..2..0
..2..2..2..2..1..0..2. .1..2..1..1..1..2..1. .2..0..2..2..1..0..2
..0..1..0..1..0..1..1. .2..1..2..2..2..1..2. .0..1..0..1..0..1..1

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

Cf. A275228.

A275229 Number of 3 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

2, 11, 61, 339, 1885, 10483, 58301, 324243, 1803293, 10029107, 55777405, 310208979, 1725243613, 9595033459, 53363285309, 296782729491, 1650572823965, 9179747931827, 51053652931069, 283937587062867, 1579133885991517

Offset: 1

R. H. Hardin, Jul 20 2016

nonn

			Some solutions for n=4:
..0..1..1..0. .0..1..1..1. .0..1..0..1. .0..0..0..0. .0..1..2..1
..2..0..0..1. .1..0..2..2. .2..0..1..0. .1..2..1..1. .1..0..1..0
..0..2..2..2. .2..2..0..0. .0..1..0..2. .2..1..2..2. .2..1..2..1

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

Row 3 of A275228.

Empirical: a(n) = 7*a(n-1) - 8*a(n-2).
Conjectures from Colin Barker, Feb 02 2019: (Start)
G.f.: x*(2 - 3*x) / (1 - 7*x + 8*x^2).
a(n) = (2^(-4-n) * ((7-sqrt(17))^n * (-11+3*sqrt(17)) + (7+sqrt(17))^n*(11+3*sqrt(17)))) / sqrt(17).
(End)

A275230 Number of 5 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

8, 66, 648, 6448, 64248, 640250, 6380362, 63583084, 633633188, 6314431394, 62926066122, 627085726484, 6249183090572, 62275838294858, 620605922265106, 6184609012036812, 61632329405048644, 614193075180580914

Offset: 1

R. H. Hardin, Jul 20 2016

nonn

			Some solutions for n=4:
..0..1..2..0. .0..0..1..2. .0..1..0..1. .0..1..0..2. .0..1..2..1
..1..2..1..2. .2..1..0..1. .1..0..1..0. .1..0..1..0. .1..2..1..2
..0..1..2..0. .1..2..1..2. .0..2..0..1. .0..1..0..2. .2..1..0..1
..1..2..0..2. .2..1..2..1. .2..0..1..2. .1..0..1..0. .1..2..1..2
..0..1..2..0. .1..0..1..2. .1..2..0..1. .0..2..0..2. .2..1..2..1

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

Row 5 of A275228.

Empirical: a(n) = 11*a(n-1) - 9*a(n-2) - 15*a(n-3) + 20*a(n-4) - 6*a(n-5) for n>6.

Empirical g.f.: 2*x*(4 - 11*x - 3*x^2 + 17*x^3 - 9*x^4 + x^5) / ((1 - x)*(1 - 10*x - x^2 + 14*x^3 - 6*x^4)). - Colin Barker, Feb 02 2019

A275231 Number of 6 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

16, 162, 2282, 32388, 460034, 6534900, 92831330, 1318716132, 18733040162, 266112481908, 3780264894914, 53700610406820, 762844837516610, 10836603937486452, 153939541994209442, 2186790504309773028

Offset: 1

R. H. Hardin, Jul 20 2016

nonn

			Some solutions for n=4:
..0..0..1..2. .0..1..2..2. .0..1..0..1. .0..1..2..1. .0..1..2..1
..2..1..2..1. .1..0..1..0. .2..0..1..0. .1..2..1..0. .2..2..1..2
..1..2..1..2. .2..1..0..1. .0..2..0..2. .0..1..0..1. .0..1..2..0
..2..1..0..1. .1..0..1..0. .1..0..2..0. .1..0..1..0. .1..0..1..2
..1..2..1..0. .0..1..2..2. .0..1..1..1. .0..1..2..1. .0..1..2..1
..2..1..2..1. .1..2..1..0. .1..0..2..0. .1..0..1..2. .2..2..1..0

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

Row 6 of A275228.

Empirical: a(n) = 19*a(n-1) - 75*a(n-2) + 101*a(n-3) - 44*a(n-4) for n>5.

Empirical g.f.: 2*x*(8 - 71*x + 202*x^2 - 218*x^3 + 77*x^4) / ((1 - x)*(1 - 18*x + 57*x^2 - 44*x^3)). - Colin Barker, Feb 02 2019

A275232 Number of 7Xn 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

32, 404, 8134, 164645, 3334854, 67550874, 1368326231, 27717164160, 561446064338, 11372797129197, 230370331746218, 4666441245648374, 94524645450606455, 1914715759242977500, 38784979537110927630, 785638615177198244373

Offset: 1

R. H. Hardin, Jul 20 2016

nonn

Row 7 of A275228.

			Some solutions for n=4
..0..1..0..2. .0..1..0..2. .0..0..0..1. .0..1..0..0. .0..1..0..0
..1..0..1..1. .2..0..1..0. .1..2..1..0. .2..2..1..2. .1..2..1..2
..0..2..0..2. .0..1..0..1. .2..1..2..1. .0..1..2..1. .2..1..2..1
..2..0..2..0. .2..0..2..0. .1..2..1..0. .1..0..0..2. .1..2..1..2
..0..2..0..2. .0..2..0..1. .2..1..2..1. .2..1..2..1. .2..1..2..1
..2..0..2..0. .1..0..2..0. .1..2..1..2. .1..2..1..2. .1..2..1..0
..1..2..1..1. .0..1..0..1. .2..1..2..1. .2..1..0..1. .0..0..0..1

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

Cf. A275228.

Empirical: a(n) = 20*a(n-1) +57*a(n-2) -1206*a(n-3) +3096*a(n-4) +2306*a(n-5) -16957*a(n-6) +20440*a(n-7) -7755*a(n-8) for n>9

cp's OEIS Frontend

A275222 Number of n X 2 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,0) and new values introduced in order 0..2.

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A275223 Number of nX3 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,0) and new values introduced in order 0..2.

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A275224 Number of nX4 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,0) and new values introduced in order 0..2.

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A275225 Number of nX5 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,0) and new values introduced in order 0..2.

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A275226 Number of nX6 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,0) and new values introduced in order 0..2.

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A275227 Number of nX7 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,0) and new values introduced in order 0..2.

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A275229 Number of 3 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,0) and new values introduced in order 0..2.

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A275230 Number of 5 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,0) and new values introduced in order 0..2.

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A275231 Number of 6 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,0) and new values introduced in order 0..2.

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A275232 Number of 7Xn 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,0) and new values introduced in order 0..2.

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