A274749 -id:A274749 - cp's OEIS frontend

A274745 Number of n X 4 0..2 arrays with no element equal to any value at offset (-1,-2) (0,-1) or (-1,0) and new values introduced in order 0..2.

4, 22, 133, 813, 4967, 30349, 185435, 1133025, 6922887, 42299477, 258453699, 1579175897, 9648910127, 58955729261, 360224933899, 2201007512401, 13448358549783, 82170708943301, 502070597184787, 3067697574952457

Offset: 1

R. H. Hardin, Jul 04 2016

nonn

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

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

Column 4 of A274749.

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

Empirical g.f.: x*(1 - x)*(4 + 2*x - x^2) / (1 - 6*x - x^2 + 2*x^3). - Colin Barker, Jan 30 2019

A274746 Number of n X 5 0..2 arrays with no element equal to any value at offset (-1,-2) (0,-1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

8, 60, 518, 4554, 40242, 355504, 3140840, 27748676, 245154340, 2165891856, 19135242632, 169056228008, 1493579612136, 13195491722256, 116579658950800, 1029959107782112, 9099492769592768, 80392287459022000, 710250565228311920

Offset: 1

R. H. Hardin, Jul 04 2016

nonn

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

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

Column 5 of A274749.

Empirical: a(n) = 9*a(n-1) - 14*a(n-3) + 10*a(n-4) - 2*a(n-5) for n>6.

Empirical g.f.: 2*x*(4 - 6*x - 11*x^2 + 2*x^3 + 8*x^4 - 3*x^5) / (1 - 9*x + 14*x^3 - 10*x^4 + 2*x^5). - Colin Barker, Jan 30 2019

A274747 Number of nX6 0..2 arrays with no element equal to any value at offset (-1,-2) (0,-1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

16, 164, 2017, 25585, 327123, 4190533, 53680592, 687685512, 8809672678, 112857546696, 1445776873145, 18521322045287, 237269920345659, 3039578666135430, 38938936908037372, 498832560169009277

Offset: 1

R. H. Hardin, Jul 04 2016

nonn

Column 6 of A274749.

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

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

Cf. A274749.

Empirical: a(n) = 14*a(n-1) -10*a(n-2) -80*a(n-3) +177*a(n-4) -152*a(n-5) +56*a(n-6) -a(n-7) -5*a(n-8) +a(n-9) for n>11

A274748 Number of nX7 0..2 arrays with no element equal to any value at offset (-1,-2) (0,-1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

32, 448, 7858, 143634, 2661918, 49475642, 920432562, 17123659885, 318581114142, 5927090659144, 110271727008501, 2051571144042267, 38168848457457660, 710119627548581257, 13211556323824865000, 245796923794474296948

Offset: 1

R. H. Hardin, Jul 04 2016

nonn

Column 7 of A274749.

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

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

Cf. A274749.

Empirical: a(n) = 21*a(n-1) -27*a(n-2) -407*a(n-3) +1614*a(n-4) -2305*a(n-5) +777*a(n-6) +1788*a(n-7) -2530*a(n-8) +1209*a(n-9) +56*a(n-10) -295*a(n-11) +115*a(n-12) -15*a(n-13) for n>15

A274750 Number of 3 X n 0..2 arrays with no element equal to any value at offset (-1,-2) (0,-1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

2, 9, 34, 133, 518, 2017, 7858, 30605, 119214, 464345, 1808682, 7044997, 27441030, 106885713, 416331266, 1621654589, 6316517406, 24603508041, 95833284570, 373280851061, 1453968675382, 5663362861249, 22059401583154, 85923718843693

Offset: 1

R. H. Hardin, Jul 04 2016

nonn

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

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

Row 3 of A274749.

Empirical: a(n) = 2*a(n-1) + 7*a(n-2) + 2*a(n-3) - 2*a(n-4).

Empirical g.f.: x*(2 + 5*x + 2*x^2 - 2*x^3) / ((1 + x)*(1 - 3*x - 4*x^2 + 2*x^3)). - Colin Barker, Jan 30 2019

A274751 Number of 4 X n 0..2 arrays with no element equal to any value at offset (-1,-2) (0,-1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

4, 27, 144, 813, 4554, 25585, 143634, 806695, 4529786, 25438375, 142850048, 802197187, 4504820208, 25297392889, 142060454416, 797757713921, 4479903521254, 25157436233205, 141274594599246, 793344420605515

Offset: 1

R. H. Hardin, Jul 04 2016

nonn

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

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

Row 4 of A274749.

Empirical: a(n) = 2*a(n-1) + 20*a(n-2) + 10*a(n-3) - 44*a(n-4) - 20*a(n-5) + 31*a(n-6) + 2*a(n-7) - 4*a(n-8).

Empirical g.f.: x*(4 + 19*x + 10*x^2 - 55*x^3 - 46*x^4 + 45*x^5 + 6*x^6 - 6*x^7) / ((1 + x - x^2)*(1 - 3*x - 16*x^2 + 3*x^3 + 25*x^4 - 2*x^5 - 4*x^6)). - Colin Barker, Jan 30 2019

A274752 Number of 5Xn 0..2 arrays with no element equal to any value at offset (-1,-2) (0,-1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

8, 81, 610, 4967, 40242, 327123, 2661918, 21656459, 176259458, 1434313078, 11673115263, 94995850464, 773101634059, 6291606309132, 51202379223709, 416693699123591, 3391131540449104, 27597636527429286, 224594629125220765

Offset: 1

R. H. Hardin, Jul 04 2016

nonn

Row 5 of A274749.

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

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

Cf. A274749.

Empirical: a(n) = 2*a(n-1) +55*a(n-2) +38*a(n-3) -614*a(n-4) -600*a(n-5) +2769*a(n-6) +2140*a(n-7) -6482*a(n-8) -2606*a(n-9) +7803*a(n-10) +678*a(n-11) -4266*a(n-12) +304*a(n-13) +924*a(n-14) -72*a(n-15) -72*a(n-16) for n>17

A274753 Number of 6Xn 0..2 arrays with no element equal to any value at offset (-1,-2) (0,-1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

16, 243, 2584, 30349, 355504, 4190533, 49475642, 584676706, 6910844226, 81707047512, 965986300341, 11421440282793, 135038015584259, 1596629353977271, 18877567144827169, 223198901191401063

Offset: 1

R. H. Hardin, Jul 04 2016

nonn

Row 6 of A274749.

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

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

Cf. A274749.

Empirical: a(n) = 2*a(n-1) +152*a(n-2) +126*a(n-3) -6741*a(n-4) -9730*a(n-5) +144236*a(n-6) +211544*a(n-7) -1827425*a(n-8) -2254882*a(n-9) +15047732*a(n-10) +13461608*a(n-11) -83672422*a(n-12) -46079542*a(n-13) +318146254*a(n-14) +83743568*a(n-15) -832325842*a(n-16) -43299570*a(n-17) +1510818060*a(n-18) -133037018*a(n-19) -1921914874*a(n-20) +326729576*a(n-21) +1726512331*a(n-22) -355689576*a(n-23) -1096976553*a(n-24) +226215282*a(n-25) +489155842*a(n-26) -88109294*a(n-27) -149920421*a(n-28) +20717362*a(n-29) +30372727*a(n-30) -2785542*a(n-31) -3809133*a(n-32) +191694*a(n-33) +263142*a(n-34) -5112*a(n-35) -7560*a(n-36) for n>38

A274754 Number of 7Xn 0..2 arrays with no element equal to any value at offset (-1,-2) (0,-1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

32, 729, 10946, 185435, 3140840, 53680592, 920432562, 15806543610, 271711836855, 4671914239590, 80354505513874, 1382068876451987, 23773417216542030, 408926400535170333, 7034177852486985161, 120997474917708497554

Offset: 1

R. H. Hardin, Jul 04 2016

nonn

Row 7 of A274749.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 80

Cf. A274749.

Empirical recurrence of order 80 (see link above)

A274744 Number of n X n 0..2 arrays with no element equal to any value at offset (-1,-2), (0,-1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

1, 3, 34, 813, 40242, 4190533, 920432562, 427529873959, 420708712370442, 878018029249193808, 3889681900917706414509, 36599212212994279601355491, 731787586726658710118188021426

Offset: 1

R. H. Hardin, Jul 04 2016

nonn

Diagonal of A274749.

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

Cf. A274749.

cp's OEIS Frontend

A274745 Number of n X 4 0..2 arrays with no element equal to any value at offset (-1,-2) (0,-1) or (-1,0) and new values introduced in order 0..2.

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A274746 Number of n X 5 0..2 arrays with no element equal to any value at offset (-1,-2) (0,-1) or (-1,0) and new values introduced in order 0..2.

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A274747 Number of nX6 0..2 arrays with no element equal to any value at offset (-1,-2) (0,-1) or (-1,0) and new values introduced in order 0..2.

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A274748 Number of nX7 0..2 arrays with no element equal to any value at offset (-1,-2) (0,-1) or (-1,0) and new values introduced in order 0..2.

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A274750 Number of 3 X n 0..2 arrays with no element equal to any value at offset (-1,-2) (0,-1) or (-1,0) and new values introduced in order 0..2.

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A274751 Number of 4 X n 0..2 arrays with no element equal to any value at offset (-1,-2) (0,-1) or (-1,0) and new values introduced in order 0..2.

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A274752 Number of 5Xn 0..2 arrays with no element equal to any value at offset (-1,-2) (0,-1) or (-1,0) and new values introduced in order 0..2.

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A274753 Number of 6Xn 0..2 arrays with no element equal to any value at offset (-1,-2) (0,-1) or (-1,0) and new values introduced in order 0..2.

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A274754 Number of 7Xn 0..2 arrays with no element equal to any value at offset (-1,-2) (0,-1) or (-1,0) and new values introduced in order 0..2.

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A274744 Number of n X n 0..2 arrays with no element equal to any value at offset (-1,-2), (0,-1) or (-1,0) and new values introduced in order 0..2.

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