A220632 -id:A220632 - cp's OEIS frontend

A220628 Number of ways to reciprocally link elements of an n X n array either to themselves or to exactly two horizontal or antidiagonal neighbors.

1, 1, 3, 37, 1481, 183961, 72097810, 91163971015, 374610359478958, 4999831941923800805, 216409223358914018252290, 30357148112130816204187346595, 13800400036239294148735727438211949

Offset: 1

R. H. Hardin, Dec 17 2012

nonn

Diagonal of A220632.

			All solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10)
.00.67.47...00.00.00...00.00.00
.36.34.00...00.67.47...00.00.00
.00.00.00...36.34.00...00.00.00

R. H. Hardin, Table of n, a(n) for n = 1..16

A220629 Number of ways to reciprocally link elements of an n X 5 array either to themselves or to exactly two horizontal or antidiagonal neighbors.

Original entry on oeis.org

1, 8, 44, 257, 1481, 8560, 49448, 285669, 1650333, 9534128, 55079528, 318199485, 1838267585, 10619840324, 61351790884, 354434918989, 2047603011865, 11829190267612, 68338316351600, 394796716945057, 2280776817922653

Offset: 1

R. H. Hardin, Dec 17 2012

nonn

Column 5 of A220632.

			Some solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10):
.00.67.46.46.47...00.67.46.47.00...00.00.00.00.00...00.00.67.46.47
.36.47.00.36.47...36.46.34.67.47...00.67.46.47.00...00.37.67.34.00
.36.46.46.34.00...00.00.36.34.00...36.46.34.00.00...36.34.00.00.00

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

Cf. A220632.

Empirical: a(n) = 4*a(n-1) + 9*a(n-2) + 7*a(n-3) + 2*a(n-4) - a(n-5).

Empirical g.f.: x*(1 + 3*x - x^2)*(1 + x + x^2) / ((1 + x)*(1 - 5*x - 4*x^2 - 3*x^3 + x^4)). - Colin Barker, Aug 01 2018

A220630 Number of ways to reciprocally link elements of an nX6 array either to themselves or to exactly two horizontal or antidiagonal neighbors.

Original entry on oeis.org

1, 16, 158, 1665, 17527, 183961, 1932695, 20301254, 213251377, 2240062837, 23530357757, 247170637157, 2596361852466, 27273040848960, 286485012144200, 3009333012881404, 31611026051882958, 332052638832405598

Offset: 1

R. H. Hardin Dec 17 2012

nonn

Column 6 of A220632

			Some solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10)
.00.67.46.46.46.47...00.00.67.46.46.47...00.00.00.00.67.47...00.00.67.47.00.00
.36.46.47.00.37.00...00.36.46.47.37.00...00.00.00.36.34.00...00.37.37.67.46.47
.00.36.46.34.00.00...00.00.36.34.00.00...00.00.00.00.00.00...36.34.36.46.34.00

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

Empirical: a(n) = 7*a(n-1) +31*a(n-2) +57*a(n-3) +43*a(n-4) -3*a(n-5) -36*a(n-6) +19*a(n-7) -6*a(n-8) +a(n-9)

A220631 Number of ways to reciprocally link elements of an nX7 array either to themselves or to exactly two horizontal or antidiagonal neighbors.

Original entry on oeis.org

1, 32, 564, 10695, 201903, 3817452, 72097810, 1362188752, 25734606523, 486186026515, 9185167500820, 173528846174065, 3278357276282501, 61935676290875214, 1170106754973419295, 22105996097313109325

Offset: 1

R. H. Hardin Dec 17 2012

nonn

Column 7 of A220632

			Some solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10)
.00.00.00.00.00.67.47...00.67.47.67.47.67.47...00.67.46.47.00.67.47
.00.00.00.00.37.36.47...36.34.37.37.36.34.00...36.46.34.00.37.37.00
.00.00.00.36.46.34.00...00.36.34.00.00.00.00...00.00.00.36.34.00.00

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

Empirical: a(n) = 11*a(n-1) +119*a(n-2) +510*a(n-3) +1074*a(n-4) +735*a(n-5) -1120*a(n-6) -2716*a(n-7) +5687*a(n-8) -4250*a(n-9) +1973*a(n-10) -802*a(n-11) +244*a(n-12) -36*a(n-13) -4*a(n-14)

A220633 Number of ways to reciprocally link elements of an 3 X n array either to themselves or to exactly two horizontal or antidiagonal neighbors.

Original entry on oeis.org

1, 1, 3, 12, 44, 158, 564, 2010, 7160, 25502, 90828, 323490, 1152128, 4103366, 14614356, 52049802, 185378120, 660233966, 2351458140, 8374842354, 29827443344, 106232014742, 378350930916, 1347516822234, 4799252328536, 17092790630078

Offset: 1

R. H. Hardin, Dec 17 2012

nonn

Row 3 of A220632.

			All solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10):
.00.00.00...00.67.47...00.00.00
.00.67.47...36.34.00...00.00.00
.36.34.00...00.00.00...00.00.00

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

Cf. A220632.

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

Empirical g.f.: x*(1 - x - x^2)*(1 - 2*x - x^2) / ((1 - x)*(1 - 3*x - 2*x^2)). - Colin Barker, Aug 02 2018

A220634 Number of ways to reciprocally link elements of an 4 X n array either to themselves or to exactly two horizontal or antidiagonal neighbors.

Original entry on oeis.org

1, 1, 5, 37, 257, 1665, 10695, 68637, 440509, 2827377, 18148003, 116487861, 747713321, 4799439985, 30806785967, 197743565181, 1269282762917, 8147313444929, 52296241209451, 335680820572405, 2154679016567857

Offset: 1

R. H. Hardin, Dec 17 2012

nonn

Row 4 of A220632.

			All solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10):
.00.00.00...00.00.00...00.67.47...00.67.47...00.00.00
.00.00.00...00.00.00...36.34.00...36.34.00...00.67.47
.00.67.47...00.00.00...00.67.47...00.00.00...36.34.00
.36.34.00...00.00.00...36.34.00...00.00.00...00.00.00

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

Cf. A220632.

Empirical: a(n) = 9*a(n-1) - 16*a(n-2) - 6*a(n-3) + 15*a(n-4) + a(n-5) - 2*a(n-6) for n>9.

Empirical g.f.: x*(1 - 8*x + 12*x^2 + 14*x^3 - 5*x^4 - 42*x^5 - 30*x^6 + 6*x^7 + 4*x^8) / ((1 - x)*(1 - 2*x - x^2)*(1 - 6*x - 3*x^2 + 2*x^3)). - Colin Barker, Aug 02 2018

A220635 Number of ways to reciprocally link elements of an 5Xn array either to themselves or to exactly two horizontal or antidiagonal neighbors.

Original entry on oeis.org

1, 1, 8, 114, 1481, 17527, 201903, 2329448, 26904225, 310837917, 3591561452, 41499180881, 479508472309, 5540546671074, 64018957168901, 739714921940047, 8547125318062702, 98758781455779205, 1141120102778497151

Offset: 1

R. H. Hardin Dec 17 2012

nonn

Row 5 of A220632

			Some solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10)
.00.67.47...00.67.47...00.00.00...00.00.00...00.00.00...00.67.47...00.00.00
.36.34.00...36.34.00...00.00.00...00.67.47...00.67.47...36.34.00...00.00.00
.00.67.47...00.00.00...00.00.00...36.34.00...36.34.00...00.00.00...00.00.00
.36.34.00...00.67.47...00.67.47...00.67.47...00.00.00...00.00.00...00.00.00
.00.00.00...36.34.00...36.34.00...36.34.00...00.00.00...00.00.00...00.00.00

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

Empirical: a(n) = 16*a(n-1) -39*a(n-2) -186*a(n-3) +419*a(n-4) +1024*a(n-5) -1049*a(n-6) -2258*a(n-7) +861*a(n-8) +2000*a(n-9) -133*a(n-10) -586*a(n-11) -16*a(n-12) +32*a(n-13) for n>17

A220636 Number of ways to reciprocally link elements of an 6Xn array either to themselves or to exactly two horizontal or antidiagonal neighbors.

Original entry on oeis.org

1, 1, 13, 351, 8560, 183961, 3817452, 79063898, 1643423543, 34184820039, 711142299027, 14793696906106, 307746212613995, 6401868705356519, 133174202661890384, 2770341001987547086, 57629691849567578540

Offset: 1

R. H. Hardin Dec 17 2012

nonn

Row 6 of A220632

			Some solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10)
.00.67.47...00.67.47...00.67.47...00.00.00...00.00.00...00.00.00...00.67.47
.36.34.00...36.34.00...36.34.00...00.67.47...00.00.00...00.00.00...36.34.00
.00.00.00...00.67.47...00.00.00...36.34.00...00.67.47...00.67.47...00.00.00
.00.00.00...36.34.00...00.00.00...00.00.00...36.34.00...36.34.00...00.67.47
.00.67.47...00.00.00...00.00.00...00.00.00...00.67.47...00.00.00...36.34.00
.36.34.00...00.00.00...00.00.00...00.00.00...36.34.00...00.00.00...00.00.00

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

Empirical: a(n) = 32*a(n-1) -195*a(n-2) -1350*a(n-3) +10665*a(n-4) +31692*a(n-5) -206199*a(n-6) -507142*a(n-7) +1799954*a(n-8) +4606048*a(n-9) -7358332*a(n-10) -21711948*a(n-11) +13920815*a(n-12) +54513592*a(n-13) -9084809*a(n-14) -73913886*a(n-15) -4653883*a(n-16) +53601160*a(n-17) +7698097*a(n-18) -21029870*a(n-19) -3072503*a(n-20) +4411176*a(n-21) +533603*a(n-22) -476894*a(n-23) -41967*a(n-24) +24240*a(n-25) +1155*a(n-26) -450*a(n-27) for n>32

A220637 Number of ways to reciprocally link elements of an 7Xn array either to themselves or to exactly two horizontal or antidiagonal neighbors.

Original entry on oeis.org

1, 1, 21, 1081, 49448, 1932695, 72097810, 2685329069, 100377946990, 3759405889469, 140807441642550, 5273589943694582, 197503772671988555, 7396752550237211667, 277016765034509275485, 10374589395033217351070

Offset: 1

R. H. Hardin Dec 17 2012

nonn

Row 7 of A220632

			Some solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10)
.00.00.00...00.00.00...00.67.47...00.00.00...00.67.47...00.00.00...00.00.00
.00.00.00...00.67.47...36.34.00...00.00.00...36.34.00...00.67.47...00.00.00
.00.00.00...36.34.00...00.00.00...00.67.47...00.67.47...36.34.00...00.00.00
.00.00.00...00.00.00...00.67.47...36.34.00...36.34.00...00.00.00...00.00.00
.00.67.47...00.00.00...36.34.00...00.67.47...00.67.47...00.00.00...00.00.00
.36.34.00...00.67.47...00.67.47...36.34.00...36.34.00...00.00.00...00.67.47
.00.00.00...36.34.00...36.34.00...00.00.00...00.00.00...00.00.00...36.34.00

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

Empirical: a(n) = 64*a(n-1) -919*a(n-2) -8570*a(n-3) +216353*a(n-4) +531044*a(n-5) -21261655*a(n-6) -32609802*a(n-7) +1171199810*a(n-8) +2109648488*a(n-9) -39063293438*a(n-10) -92688824988*a(n-11) +805714999129*a(n-12) +2451647584900*a(n-13) -10235971284893*a(n-14) -39686089670614*a(n-15) +77545474788177*a(n-16) +406392430654220*a(n-17) -310370552865987*a(n-18) -2718695732195110*a(n-19) +210699841602232*a(n-20) +12228246476518236*a(n-21) +4161966890556370*a(n-22) -37977869919855064*a(n-23) -22915950784622786*a(n-24) +83551109201976972*a(n-25) +64155355218097920*a(n-26) -133459785405218204*a(n-27) -114791737399493541*a(n-28) +158383696504733072*a(n-29) +141093830957446007*a(n-30) -142389992780977126*a(n-31) -123172425999322826*a(n-32) +98262359403451972*a(n-33) +77694058934774432*a(n-34) -52288937671239360*a(n-35) -35710455324063520*a(n-36) +21366553927398268*a(n-37) +11998414558707900*a(n-38) -6636734211915116*a(n-39) -2945615880166783*a(n-40) +1547201872012720*a(n-41) +525999708944081*a(n-42) -266869650005278*a(n-43) -67611096067185*a(n-44) +33461039766336*a(n-45) +6135683963135*a(n-46) -2975024785990*a(n-47) -380281115163*a(n-48) +180562165772*a(n-49) +15221629883*a(n-50) -7030915042*a(n-51) -357383528*a(n-52) +157690672*a(n-53) +4153756*a(n-54) -1668248*a(n-55) -18816*a(n-56) +6272*a(n-57) for n>63

cp's OEIS Frontend

A220628 Number of ways to reciprocally link elements of an n X n array either to themselves or to exactly two horizontal or antidiagonal neighbors.

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A220629 Number of ways to reciprocally link elements of an n X 5 array either to themselves or to exactly two horizontal or antidiagonal neighbors.

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A220630 Number of ways to reciprocally link elements of an nX6 array either to themselves or to exactly two horizontal or antidiagonal neighbors.

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A220631 Number of ways to reciprocally link elements of an nX7 array either to themselves or to exactly two horizontal or antidiagonal neighbors.

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A220633 Number of ways to reciprocally link elements of an 3 X n array either to themselves or to exactly two horizontal or antidiagonal neighbors.

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A220634 Number of ways to reciprocally link elements of an 4 X n array either to themselves or to exactly two horizontal or antidiagonal neighbors.

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A220635 Number of ways to reciprocally link elements of an 5Xn array either to themselves or to exactly two horizontal or antidiagonal neighbors.

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A220636 Number of ways to reciprocally link elements of an 6Xn array either to themselves or to exactly two horizontal or antidiagonal neighbors.

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A220637 Number of ways to reciprocally link elements of an 7Xn array either to themselves or to exactly two horizontal or antidiagonal neighbors.

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