A220708 -id:A220708 - cp's OEIS frontend

A220704 Number of ways to reciprocally link elements of an n X n array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.

1, 1, 3, 13, 107, 1617, 44976, 2282408, 216083336, 37166744488, 11934907610044, 6974153590170208, 7595477025017870022, 15083748097547577433271, 55729708477784939752304144, 376141278066033748724918163244

Offset: 1

R. H. Hardin Dec 18 2012

nonn

Diagonal of A220708

			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
.00.00.00...36.34.00...00.67.47
.00.00.00...00.00.00...36.34.00

R. H. Hardin, Table of n, a(n) for n = 1..18

A220705 Number of ways to reciprocally link elements of an n X 5 array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.

Original entry on oeis.org

1, 5, 12, 37, 107, 317, 932, 2749, 8101, 23881, 70392, 207497, 611639, 1802937, 5314536, 15665721, 46178025, 136119501, 401241028, 1182742829, 3486384739, 10276856693, 30293209548, 89295644789, 263217806797, 775890178961

Offset: 1

R. H. Hardin, Dec 18 2012

nonn

Column 5 of A220708.

			Some solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10):
.00.00.67.47.00...00.00.00.00.00...00.00.00.00.00...00.67.47.00.00
.00.36.34.67.47...00.67.47.67.47...00.00.00.00.00...36.34.00.00.00
.00.00.36.34.00...36.34.36.34.00...00.00.00.00.00...00.00.00.00.00

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

Cf. A220708.

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

Empirical g.f.: x*(1 + 3*x - x^2 - 2*x^3 - 2*x^4 - x^5) / ((1 - x)*(1 + x)*(1 - 2*x - 2*x^2 - 2*x^3 - x^4)). - Colin Barker, Aug 02 2018

A220706 Number of ways to reciprocally link elements of an n X 6 array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.

Original entry on oeis.org

1, 8, 24, 105, 405, 1617, 6412, 25449, 101029, 400986, 1591697, 6317904, 25077948, 99542634, 395117919, 1568354512, 6225321052, 24710371599, 98083689723, 389326813396, 1545367714146, 6134078853549, 24348200775585, 96646113488531

Offset: 1

R. H. Hardin, Dec 18 2012

nonn

Column 6 of A220708.

			Some solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10):
.00.00.67.47.67.47...00.00.00.00.67.47...00.00.00.00.00.00...00.00.00.00.00.00
.00.36.34.36.34.00...00.67.47.36.34.00...00.00.67.47.67.47...00.00.00.00.00.00
.00.00.00.00.00.00...36.34.00.00.00.00...00.36.34.36.34.00...00.00.00.00.00.00

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

Cf. A220708.

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

Empirical g.f.: x*(1 + x)*(1 + 4*x - 9*x^2 + 5*x^3 - 5*x^4 + 3*x^5 + x^6 - x^8) / (1 - 3*x - 5*x^2 + 3*x^3 + 6*x^4 + x^5 + x^6 - 4*x^7 - x^8 + x^9 + x^10). - Colin Barker, Aug 02 2018

A220707 Number of ways to reciprocally link elements of an n X 7 array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.

Original entry on oeis.org

1, 13, 48, 298, 1520, 8338, 44976, 244029, 1322551, 7171769, 38885648, 210854845, 1143330649, 6199601829, 33616711696, 182283373322, 988413912488, 5359579124490, 29061800830768, 157584813722329, 854488462716575

Offset: 1

R. H. Hardin, Dec 18 2012

nonn

Column 7 of A220708.

			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...00.00.00.00.00.00.00...00.67.47.00.00.00.00
.00.00.67.47.00.00.00...00.00.67.47.67.47.00...36.34.00.00.00.67.47
.00.36.34.00.00.00.00...00.36.34.36.34.00.00...00.00.00.00.36.34.00

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

Cf. A220708.

Empirical: a(n) = 5*a(n-1) +6*a(n-2) -17*a(n-3) -19*a(n-4) +10*a(n-5) +16*a(n-6) -46*a(n-7) +7*a(n-8) +15*a(n-9) -14*a(n-10) +21*a(n-11) +3*a(n-12) +10*a(n-13) +8*a(n-14) +2*a(n-15) +5*a(n-16) +a(n-17) +2*a(n-18) -a(n-19) -a(n-20).

A220709 Number of ways to reciprocally link elements of a 4 X n array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.

Original entry on oeis.org

1, 1, 5, 13, 37, 105, 298, 846, 2404, 6826, 19394, 55081, 156473, 444445, 1262497, 3586113, 10186570, 28935186, 82191652, 233468038, 663174914, 1883771569, 5350922525, 15199487245, 43174696525, 122639283705, 348361331050

Offset: 1

R. H. Hardin, Dec 18 2012

nonn

Row 4 of A220708.

			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
.00.67.47...00.00.00...36.34.00...36.34.00...00.00.00
.36.34.00...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

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

Cf. A220708.

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

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

A220710 Number of ways to reciprocally link elements of an 5 X n array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.

Original entry on oeis.org

1, 1, 8, 28, 107, 405, 1520, 5706, 21418, 80390, 301736, 1132543, 4250895, 15955408, 59887275, 224782132, 843701335, 3166765105, 11886195940, 44613876758, 167454575870, 628527215306, 2359126067724, 8854788952291, 33235734276043

Offset: 1

R. H. Hardin, Dec 18 2012

nonn

Row 5 of A220708.

			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...00.67.47...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...00.00.00
.36.34.00...00.00.00...00.00.00...00.00.00...00.67.47...36.34.00...00.00.00
.00.00.00...00.67.47...00.00.00...00.67.47...36.34.00...00.67.47...00.00.00
.00.00.00...36.34.00...00.00.00...36.34.00...00.00.00...36.34.00...00.00.00

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

Cf. A220708.

Empirical: a(n) = 3*a(n-1) + 7*a(n-2) - 14*a(n-3) - 11*a(n-4) + 17*a(n-5) + 5*a(n-6) - 6*a(n-7) for n>11.

Empirical g.f.: x*(1 - 2*x - 2*x^2 + 11*x^3 - 8*x^4 - 6*x^5 + 14*x^6 - 18*x^7 - 3*x^8 + 18*x^9 - 8*x^10) / ((1 - x)*(1 + x)*(1 - 3*x - 6*x^2 + 11*x^3 + 5*x^4 - 6*x^5)). - Colin Barker, Aug 02 2018

A220711 Number of ways to reciprocally link elements of an 6Xn array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.

Original entry on oeis.org

1, 1, 13, 60, 317, 1617, 8338, 42873, 221082, 1139020, 5870960, 30259204, 155962396, 803874071, 4143371101, 21356146495, 110075467413, 567360680620, 2924337273221, 15072870834560, 77689863937436, 400435729023800

Offset: 1

R. H. Hardin Dec 18 2012

nonn

Row 6 of A220708

			Some 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...00.00.00...00.67.47...00.00.00...00.00.00
.36.34.00...00.67.47...00.00.00...00.00.00...36.34.00...00.67.47...00.00.00
.00.00.00...36.34.00...00.00.00...00.00.00...00.67.47...36.34.00...00.67.47
.00.67.47...00.67.47...00.00.00...00.00.00...36.34.00...00.00.00...36.34.00
.36.34.00...36.34.00...00.00.00...00.67.47...00.00.00...00.00.00...00.00.00
.00.00.00...00.00.00...00.00.00...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) = a(n-1) +33*a(n-2) -a(n-3) -351*a(n-4) -75*a(n-5) +1760*a(n-6) +436*a(n-7) -4708*a(n-8) -997*a(n-9) +6997*a(n-10) +1085*a(n-11) -5748*a(n-12) -564*a(n-13) +2512*a(n-14) +131*a(n-15) -543*a(n-16) -7*a(n-17) +49*a(n-18) -a(n-19) -a(n-20) for n>24

A220712 Number of ways to reciprocally link elements of an 7Xn array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.

Original entry on oeis.org

1, 1, 21, 129, 932, 6412, 44976, 311193, 2168111, 15034974, 104478616, 725286308, 5037269200, 34977393156, 242898931716, 1686719471828, 11713075485508, 81338093590180, 564832581201972, 3922330554994484, 27237632538545092

Offset: 1

R. H. Hardin Dec 18 2012

nonn

Row 7 of A220708

			Some 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...00.67.47...00.67.47...00.67.47...00.00.00
.36.34.00...00.00.00...00.67.47...36.34.00...36.34.00...36.34.00...00.00.00
.00.00.00...00.67.47...36.34.00...00.67.47...00.67.47...00.67.47...00.67.47
.00.00.00...36.34.00...00.00.00...36.34.00...36.34.00...36.34.00...36.34.00
.00.00.00...00.00.00...00.67.47...00.00.00...00.00.00...00.67.47...00.00.00
.00.00.00...00.00.00...36.34.00...00.67.47...00.00.00...36.34.00...00.67.47
.00.00.00...00.00.00...00.00.00...36.34.00...00.00.00...00.00.00...36.34.00

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

Empirical: a(n) = a(n-1) +76*a(n-2) -4*a(n-3) -2156*a(n-4) -520*a(n-5) +32432*a(n-6) +9800*a(n-7) -296352*a(n-8) -80128*a(n-9) +1755472*a(n-10) +365536*a(n-11) -6970672*a(n-12) -1003248*a(n-13) +18839680*a(n-14) +1679040*a(n-15) -34716928*a(n-16) -1650048*a(n-17) +43135744*a(n-18) +820736*a(n-19) -35163136*a(n-20) -61440*a(n-21) +17813504*a(n-22) -116736*a(n-23) -5017600*a(n-24) +36864*a(n-25) +589824*a(n-26) for n>32

cp's OEIS Frontend

A220704 Number of ways to reciprocally link elements of an n X n array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.

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A220705 Number of ways to reciprocally link elements of an n X 5 array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.

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A220706 Number of ways to reciprocally link elements of an n X 6 array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.

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A220707 Number of ways to reciprocally link elements of an n X 7 array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.

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A220709 Number of ways to reciprocally link elements of a 4 X n array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.

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A220710 Number of ways to reciprocally link elements of an 5 X n array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.

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A220711 Number of ways to reciprocally link elements of an 6Xn array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.

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A220712 Number of ways to reciprocally link elements of an 7Xn array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.

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Examples

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