A220553 -id:A220553 - cp's OEIS frontend

A220547 Number of ways to reciprocally link elements of an n X 2 array either to themselves or to exactly one horizontal, vertical or antidiagonal neighbor.

2, 8, 29, 108, 401, 1490, 5536, 20569, 76424, 283953, 1055026, 3919944, 14564533, 54114452, 201061985, 747044834, 2775641472, 10312882481, 38317465040, 142368356257, 528968939938, 1965381541064, 7302365621709, 27131904192124

Offset: 1

R. H. Hardin, Dec 15 2012

nonn

Column 2 of A220553.

			Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10):
..8..8....0..7....6..4....6..4....8..0....0..0....0..0....0..0....0..8....6..4
..2..2....3..8....0..0....6..4....2..8....8..8....0..8....0..0....8..2....8..8
..6..4....0..2....0..0....0..0....0..2....2..2....0..2....0..0....2..0....2..2

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

Cf. A220553, A000078.

Empirical: a(n) = 3*a(n-1) + 3*a(n-2) - a(n-3) - a(n-4).
Empirical g.f.: x*(1 + x)*(2 - x^2) / (1 - 3*x - 3*x^2 + x^3 + x^4). - Colin Barker, Mar 13 2018
Empirical: a(n) = A000078(2*n + 3). - Greg Dresden, Jan 10 2021

A220546 Number of ways to reciprocally link elements of an n X n array either to themselves or to exactly one horizontal, vertical or antidiagonal neighbor.

Original entry on oeis.org

1, 8, 224, 32173, 21668208, 69961268156, 1077372801893440, 79222784184855853978, 27809964251933826835780981, 46605836505704256743057461864323

Offset: 1

R. H. Hardin Dec 15 2012

nonn

Diagonal of A220553

			Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10)
..0..8..8....0..0..8....6..4..7....8..0..0....6..4..0....8..6..4....0..0..7
..8..2..2....0..7..2....8..3..0....2..8..8....0..7..0....2..8..0....0..3..0
..2..0..0....3..0..0....2..0..0....0..2..2....3..6..4....0..2..0....0..6..4

R. H. Hardin, Table of n, a(n) for n = 1..12

A220548 Number of ways to reciprocally link elements of an n X 3 array either to themselves or to exactly one horizontal, vertical or antidiagonal neighbor.

Original entry on oeis.org

3, 29, 224, 1814, 14556, 117022, 940432, 7558245, 60744605, 488197825, 3923590632, 31533457665, 253430854415, 2036795298237, 16369494914388, 131559791031398, 1057331255850916, 8497652480629342, 68294678022457540, 548876652325439237

Offset: 1

R. H. Hardin, Dec 15 2012

nonn

Column 3 of A220553.

			Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10):
..0..7..7....0..0..0....0..8..8....8..0..0....8..6..4....6..4..7....0..0..7
..3..3..0....8..6..4....8..2..2....2..0..8....2..6..4....0..3..7....8..3..7
..0..0..0....2..6..4....2..0..0....6..4..2....0..6..4....0..3..0....2..3..0

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

Cf. A220553.

Empirical: a(n) = 6*a(n-1) + 17*a(n-2) - 3*a(n-3) - 17*a(n-4) + 3*a(n-5) + 4*a(n-6) - a(n-7).

Empirical g.f.: x*(3 + 11*x - x^2 - 14*x^3 + 2*x^4 + 4*x^5 - x^6) / ((1 + x - x^2)*(1 - 7*x - 9*x^2 + 5*x^3 + 3*x^4 - x^5)). - Colin Barker, Jul 31 2018

A220549 Number of ways to reciprocally link elements of an nX4 array either to themselves or to exactly one horizontal, vertical or antidiagonal neighbor.

Original entry on oeis.org

5, 108, 1814, 32173, 565061, 9943416, 174911750, 3077034244, 54130248568, 952245176313, 16751640356635, 294690365449276, 5184113807856060, 91197538858856819, 1604322628219475789, 28222813114190945744

Offset: 1

R. H. Hardin Dec 15 2012

nonn

Column 4 of A220553

			Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10)
..6..4..7..8....0..0..6..4....6..4..7..7....8..8..0..7....6..4..7..7
..0..3..0..2....0..7..0..8....0..3..3..0....2..2..3..0....0..3..3..0
..6..4..6..4....3..0..0..2....6..4..0..0....0..0..0..0....6..4..6..4

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

Empirical: a(n) = 11*a(n-1) +111*a(n-2) +127*a(n-3) -649*a(n-4) -981*a(n-5) +1615*a(n-6) +2067*a(n-7) -2349*a(n-8) -1177*a(n-9) +1383*a(n-10) +199*a(n-11) -337*a(n-12) +3*a(n-13) +31*a(n-14) -a(n-15) -a(n-16)

A220550 Number of ways to reciprocally link elements of an nX5 array either to themselves or to exactly one horizontal, vertical or antidiagonal neighbor.

Original entry on oeis.org

8, 401, 14556, 565061, 21668208, 832899775, 32001129185, 1229633337183, 47247493674864, 1815445803499208, 69756959373004005, 2680352078247056300, 102990256079543046348, 3957313286001327139326, 152056408321267850998276

Offset: 1

R. H. Hardin Dec 15 2012

nonn

Column 5 of A220553

			Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10)
..0..7..0..0..7....0..6..4..8..8....8..6..4..0..0....8..0..8..0..7
..3..6..4..3..7....0..0..8..2..2....2..7..8..0..7....2..0..2..3..0
..6..4..0..3..0....6..4..2..6..4....3..0..2..3..0....0..0..0..6..4

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

Empirical: a(n) = 21*a(n-1) +607*a(n-2) +2818*a(n-3) -13422*a(n-4) -102307*a(n-5) +102787*a(n-6) +1377367*a(n-7) -625026*a(n-8) -9368158*a(n-9) +6655110*a(n-10) +30101928*a(n-11) -31218870*a(n-12) -45617582*a(n-13) +65294634*a(n-14) +29766481*a(n-15) -68435485*a(n-16) -4100689*a(n-17) +40652394*a(n-18) -5180290*a(n-19) -14692966*a(n-20) +3231432*a(n-21) +3351718*a(n-22) -849954*a(n-23) -490034*a(n-24) +118041*a(n-25) +45619*a(n-26) -8829*a(n-27) -2574*a(n-28) +334*a(n-29) +79*a(n-30) -5*a(n-31) -a(n-32)

A220551 Number of ways to reciprocally link elements of an nX6 array either to themselves or to exactly one horizontal, vertical or antidiagonal neighbor.

Original entry on oeis.org

13, 1490, 117022, 9943416, 832899775, 69961268156, 5873481159019, 493147308003276, 41404696495593733, 3476354713685117295, 291875923358702188677, 24506004816897100837250, 2057532704150988606181644

Offset: 1

R. H. Hardin Dec 15 2012

nonn

Column 6 of A220553

			Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10)
..6..4..7..0..8..0....0..0..0..6..4..8....0..8..0..0..0..7....8..0..0..0..8..8
..8..3..6..4..2..7....6..4..0..6..4..2....0..2..0..8..3..0....2..0..0..8..2..2
..2..6..4..0..3..0....0..0..0..0..0..0....6..4..0..2..0..0....0..6..4..2..0..0

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

Empirical: a(n) = 43*a(n-1) +3071*a(n-2) +35931*a(n-3) -339473*a(n-4) -7161173*a(n-5) +10510607*a(n-6) +579287390*a(n-7) -86009834*a(n-8) -26973137653*a(n-9) +17922247043*a(n-10) +759668332883*a(n-11) -1458641637557*a(n-12) -10811736525989*a(n-13) +34648043396638*a(n-14) +69138971017482*a(n-15) -378744880646789*a(n-16) -76869384351785*a(n-17) +2257136247846663*a(n-18) -1481921417023445*a(n-19) -8203392366781665*a(n-20) +10251619124403834*a(n-21) +19428261339797202*a(n-22) -35703350984991269*a(n-23) -30990769502166197*a(n-24) +81734131713586135*a(n-25) +33362269139093511*a(n-26) -134985540835357813*a(n-27) -23195971096184462*a(n-28) +168796132411857454*a(n-29) +8920475172874387*a(n-30) -164274545229295041*a(n-31) -1102569342380921*a(n-32) +126129771048509667*a(n-33) +1130153727733123*a(n-34) -76604004519697618*a(n-35) -3244753679232374*a(n-36) +36583369819597543*a(n-37) +3421670217601687*a(n-38) -13573387285852645*a(n-39) -2076638760328461*a(n-40) +3850117905476135*a(n-41) +830228772519594*a(n-42) -818857176583502*a(n-43) -229995045268009*a(n-44) +127535909598535*a(n-45) +45050732663975*a(n-46) -14097155555237*a(n-47) -6284132716629*a(n-48) +1051348389402*a(n-49) +624786901206*a(n-50) -47058515857*a(n-51) -44115713573*a(n-52) +699849703*a(n-53) +2192996827*a(n-54) +48467383*a(n-55) -75562626*a(n-56) -3337706*a(n-57) +1759671*a(n-58) +92567*a(n-59) -26561*a(n-60) -1265*a(n-61) +239*a(n-62) +7*a(n-63) -a(n-64)

A220552 Number of ways to reciprocally link elements of an n X 7 array either to themselves or to exactly one horizontal, vertical or antidiagonal neighbor.

Original entry on oeis.org

21, 5536, 940432, 174911750, 32001129185, 5873481159019, 1077372801893440, 197644957649145164, 36257360400073221806, 6651328207323063530996, 1220169722761405665767328, 223837152224277574339972896

Offset: 1

R. H. Hardin, Dec 15 2012

nonn

Column 7 of A220553.

			Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10)
..0..7..7..7..0..0..0....0..7..8..8..0..6..4....0..7..7..6..4..6..4
..3..3..3..7..7..7..0....3..0..2..2..0..0..7....3..3..7..0..6..4..0
..0..0..3..3..3..0..0....0..6..4..0..0..3..0....0..3..0..0..6..4..0

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

Cf. A220553.

cp's OEIS Frontend

A220547 Number of ways to reciprocally link elements of an n X 2 array either to themselves or to exactly one horizontal, vertical or antidiagonal neighbor.

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A220546 Number of ways to reciprocally link elements of an n X n array either to themselves or to exactly one horizontal, vertical or antidiagonal neighbor.

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A220548 Number of ways to reciprocally link elements of an n X 3 array either to themselves or to exactly one horizontal, vertical or antidiagonal neighbor.

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A220549 Number of ways to reciprocally link elements of an nX4 array either to themselves or to exactly one horizontal, vertical or antidiagonal neighbor.

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A220550 Number of ways to reciprocally link elements of an nX5 array either to themselves or to exactly one horizontal, vertical or antidiagonal neighbor.

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A220551 Number of ways to reciprocally link elements of an nX6 array either to themselves or to exactly one horizontal, vertical or antidiagonal neighbor.

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A220552 Number of ways to reciprocally link elements of an n X 7 array either to themselves or to exactly one horizontal, vertical or antidiagonal neighbor.

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