A274728 -id:A274728 - cp's OEIS frontend

A274723 Number of n X 3 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) or (-1,0) and new values introduced in order 0..2.

5, 24, 68, 260, 1040, 4132, 16524, 66088, 264332, 1057316, 4229264, 16917028, 67668108, 270672424, 1082689676, 4330758692, 17323034768, 69292139044, 277168556172, 1108674224680, 4434696898700, 17738787594788, 70955150379152

Offset: 1

R. H. Hardin, Jul 03 2016

nonn

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

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

Column 3 of A274728.

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

Empirical g.f.: x*(5 + 9*x - 24*x^2 - 45*x^3 - 21*x^4 - 4*x^5 + 8*x^6) / ((1 - x)*(1 + x)*(1 - 4*x)*(1 + x + x^2)). - Colin Barker, Jan 30 2019

A274724 Number of nX4 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

14, 96, 296, 1632, 9308, 52912, 301784, 1721528, 9816048, 55981988, 319253288, 1820657976, 10382921956, 59212245524, 337678318592, 1925727939552, 10982131736244, 62629418453640, 357165995693576, 2036863060347232

Offset: 1

R. H. Hardin, Jul 03 2016

nonn

Column 4 of A274728.

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

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

Cf. A274728.

Empirical: a(n) = 3*a(n-1) +13*a(n-2) +14*a(n-3) +4*a(n-4) -28*a(n-5) -13*a(n-6) -7*a(n-7) +15*a(n-8) for n>12

A274725 Number of nX5 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

41, 384, 1300, 10368, 84948, 687248, 5634776, 45990340, 375845052, 3070055916, 25083639844, 204917982144, 1674151403908, 13677241018800, 111739565720152, 912879351011812, 7457971359536024, 60929501956856368, 497776886832382136

Offset: 1

R. H. Hardin, Jul 03 2016

nonn

Column 5 of A274728.

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

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

Cf. A274728.

Empirical: a(n) = 3*a(n-1) +33*a(n-2) +66*a(n-3) +94*a(n-4) -115*a(n-5) -155*a(n-6) -255*a(n-7) +236*a(n-8) +152*a(n-9) +61*a(n-10) -213*a(n-11) +90*a(n-12) -5*a(n-13) +13*a(n-14) -4*a(n-15) for n>19

A274726 Number of nX6 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

122, 1536, 5728, 66132, 771300, 8960464, 105328812, 1237030912, 14505195904, 170291855288, 1998101079148, 23450606174376, 275190816259724, 3229562907115528, 37899889658769384, 444774756528884068

Offset: 1

R. H. Hardin, Jul 03 2016

nonn

Column 6 of A274728.

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

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

Cf. A274728.

Empirical: a(n) = 3*a(n-1) +78*a(n-2) +250*a(n-3) +558*a(n-4) -937*a(n-5) -4256*a(n-6) -7991*a(n-7) -3472*a(n-8) +31381*a(n-9) -11144*a(n-10) +42683*a(n-11) -198936*a(n-12) +231086*a(n-13) -131301*a(n-14) +70502*a(n-15) -27827*a(n-16) +159651*a(n-17) -217780*a(n-18) +120250*a(n-19) -55920*a(n-20) -17125*a(n-21) +26805*a(n-22) -25487*a(n-23) +30226*a(n-24) -15183*a(n-25) +5503*a(n-26) -1930*a(n-27) +371*a(n-28) -65*a(n-29) +8*a(n-30) for n>35

A274727 Number of nX7 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

365, 6144, 25268, 421904, 7016284, 116633012, 1980677448, 33415073716, 564905405336, 9541460598408, 161295215603556, 2725041270964876, 46055189349633552, 778212220006487596, 13151212573069796840

Offset: 1

R. H. Hardin, Jul 03 2016

nonn

Column 7 of A274728.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 59

Cf. A274728.

Empirical recurrence of order 59 (see link above)

A274729 Number of 4 X n 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

4, 48, 260, 1632, 10368, 66132, 421904, 2691884, 17175124, 109583308, 699179884, 4461012792, 28462825592, 181602806300, 1158689573772, 7392845715224, 47168947581908, 300954422923484, 1920194732348424, 12251515609312728

Offset: 1

R. H. Hardin, Jul 03 2016

nonn

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

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

Row 4 of A274728.

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

Empirical g.f.: 4*x*(1 + 4*x - 21*x^2 + 12*x^3 + 13*x^4 - 12*x^5 + 2*x^6) / ((1 - x)*(1 - 7*x + 3*x^2 + 7*x^3 - 6*x^4 + x^5)). - Colin Barker, Jan 30 2019

A274730 Number of 5 X n 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

8, 144, 1040, 9308, 84948, 771300, 7016284, 63780144, 579907180, 5272264616, 47934377596, 435805897172, 3962236677384, 36023613993928, 327517339347916, 2977702208511048, 27072492754395896, 246136048094770872

Offset: 1

R. H. Hardin, Jul 03 2016

nonn

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

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

Row 5 of A274728.

Empirical: a(n) = 10*a(n-1) - a(n-2) - 80*a(n-3) + 133*a(n-4) - 49*a(n-5) - 16*a(n-6) + 4*a(n-7) for n>9.

Empirical g.f.: 4*x*(2 + 16*x - 98*x^2 - 77*x^3 + 841*x^4 - 1108*x^5 + 434*x^6 - 72*x^7 + 24*x^8) / ((1 - x)*(1 - 9*x - 8*x^2 + 72*x^3 - 61*x^4 - 12*x^5 + 4*x^6)). - Colin Barker, Jan 30 2019

A274731 Number of 6Xn 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

16, 432, 4132, 52912, 687248, 8960464, 116633012, 1520042284, 19800817976, 257995068564, 3361220228816, 43792711784828, 570555977597820, 7433587136161392, 96849404858071388, 1261816522312628012

Offset: 1

R. H. Hardin, Jul 03 2016

nonn

Row 6 of A274728.

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

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

Cf. A274728.

Empirical: a(n) = 15*a(n-1) +a(n-2) -456*a(n-3) +1455*a(n-4) -196*a(n-5) -5263*a(n-6) +5258*a(n-7) +7193*a(n-8) -12179*a(n-9) -1317*a(n-10) +8177*a(n-11) -894*a(n-12) -2235*a(n-13) +104*a(n-14) +350*a(n-15) +27*a(n-16) -44*a(n-17) +5*a(n-18) for n>20

A274732 Number of 7Xn 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

32, 1296, 16524, 301784, 5634776, 105328812, 1980677448, 37188898120, 699226867860, 13139454740876, 246989200003420, 4642070954166124, 87252983103535936, 1639953977382243676, 30824192792654598004

Offset: 1

R. H. Hardin, Jul 03 2016

nonn

Row 7 of A274728.

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

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

Cf. A274728.

Empirical: a(n) = 21*a(n-1) +46*a(n-2) -2078*a(n-3) +7099*a(n-4) +30390*a(n-5) -199330*a(n-6) +32493*a(n-7) +1799239*a(n-8) -2883655*a(n-9) -6458651*a(n-10) +19972172*a(n-11) +4488011*a(n-12) -63185111*a(n-13) +38593516*a(n-14) +97573203*a(n-15) -147528893*a(n-16) +26937123*a(n-17) +105357461*a(n-18) -172813699*a(n-19) +142443589*a(n-20) +18232365*a(n-21) -135277945*a(n-22) +91577781*a(n-23) -13939351*a(n-24) -6667960*a(n-25) +1422372*a(n-26) +709307*a(n-27) -229702*a(n-28) +8892*a(n-29) +1296*a(n-30) for n>34

A274722 Number of n X n 0..2 arrays with no element equal to any value at offset (-1,-2), (-2,-1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

1, 6, 68, 1632, 84948, 8960464, 1980677448, 905233056800, 860544738080372, 1705630286322728068

Offset: 1

R. H. Hardin, Jul 03 2016

nonn

Diagonal of A274728.

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

Cf. A274728.

cp's OEIS Frontend

A274723 Number of n X 3 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) or (-1,0) and new values introduced in order 0..2.

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A274724 Number of nX4 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) or (-1,0) and new values introduced in order 0..2.

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A274725 Number of nX5 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) or (-1,0) and new values introduced in order 0..2.

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A274726 Number of nX6 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) or (-1,0) and new values introduced in order 0..2.

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A274727 Number of nX7 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) or (-1,0) and new values introduced in order 0..2.

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A274729 Number of 4 X n 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) or (-1,0) and new values introduced in order 0..2.

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A274730 Number of 5 X n 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) or (-1,0) and new values introduced in order 0..2.

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A274731 Number of 6Xn 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) or (-1,0) and new values introduced in order 0..2.

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A274732 Number of 7Xn 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) or (-1,0) and new values introduced in order 0..2.

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A274722 Number of n X n 0..2 arrays with no element equal to any value at offset (-1,-2), (-2,-1) or (-1,0) and new values introduced in order 0..2.