A220614 -id:A220614 - cp's OEIS frontend

A220611 Number of ways to reciprocally link elements of an n X 5 array either to themselves or to exactly two horizontal and vertical neighbors, without consecutive collinear links.

1, 8, 21, 95, 324, 1277, 4673, 17768, 66245, 249499, 934816, 3511945, 13175625, 49465544, 185641901, 696836263, 2615432756, 9816980965, 36846924297, 138302568456, 519106314333, 1948425878179, 7313254531824, 27449718110385

Offset: 1

R. H. Hardin, Dec 17 2012

nonn

Column 5 of A220614.

			Some solutions for n=3 0=self 2=n 4=w 6=e 8=s (reciprocal directions total 10):
.00.00.00.00.00...00.00.68.48.00...68.48.00.00.00...00.00.00.00.00
.68.48.00.68.48...68.48.26.24.00...26.24.68.48.00...00.00.00.68.48
.26.24.00.26.24...26.24.00.00.00...00.00.26.24.00...00.00.00.26.24

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

Cf. A220614.

Empirical: a(n) = 3*a(n-1) + 6*a(n-2) - 11*a(n-3) - 5*a(n-4) + 6*a(n-5).

Empirical g.f.: x*(1 + 5*x - 9*x^2 - 5*x^3 + 6*x^4) / (1 - 3*x - 6*x^2 + 11*x^3 + 5*x^4 - 6*x^5). - Colin Barker, Aug 01 2018

A220612 Number of ways to reciprocally link elements of an nX6 array either to themselves or to exactly two horizontal and vertical neighbors, without consecutive collinear links.

Original entry on oeis.org

1, 13, 43, 281, 1277, 7041, 34981, 183920, 937663, 4861869, 24977087, 128971605, 664092737, 3424806465, 17647051243, 90973240309, 468858278192, 2416753993341, 12456282450653, 64204249763017, 330924094972255, 1705685462529549

Offset: 1

R. H. Hardin Dec 17 2012

nonn

Column 6 of A220614

			Some solutions for n=3 0=self 2=n 4=w 6=e 8=s (reciprocal directions total 10)
.68.48.00.00.00.00...00.00.00.68.48.00...68.48.68.48.00.00...68.48.68.48.68.48
.26.24.00.00.68.48...00.00.00.26.24.00...26.24.26.24.68.48...26.24.26.24.26.24
.00.00.00.00.26.24...00.00.00.00.00.00...00.00.00.00.26.24...00.00.00.00.00.00

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

Empirical: a(n) = 3*a(n-1) +23*a(n-2) -40*a(n-3) -160*a(n-4) +190*a(n-5) +441*a(n-6) -369*a(n-7) -513*a(n-8) +278*a(n-9) +240*a(n-10) -64*a(n-11) -39*a(n-12) +3*a(n-13) +a(n-14)

A220613 Number of ways to reciprocally link elements of an nX7 array either to themselves or to exactly two horizontal and vertical neighbors, without consecutive collinear links.

Original entry on oeis.org

1, 21, 85, 781, 4673, 34981, 233265, 1653229, 11354857, 79290645, 548972737, 3817993565, 26491584361, 184040357765, 1277739038129, 8873937621293, 61619077914745, 427911161639829, 2971470559369153, 20634790487757629

Offset: 1

R. H. Hardin Dec 17 2012

nonn

Column 7 of A220614

			Some solutions for n=3 0=self 2=n 4=w 6=e 8=s (reciprocal directions total 10)
.68.48.00.68.48.00.00...68.48.68.48.00.00.00...00.00.00.68.48.00.00
.26.24.00.26.24.00.00...26.24.26.24.00.68.48...00.00.00.26.24.68.48
.00.00.00.00.00.00.00...00.00.00.00.00.26.24...00.00.00.00.00.26.24

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

Empirical: a(n) = 5*a(n-1) +40*a(n-2) -144*a(n-3) -532*a(n-4) +1484*a(n-5) +3044*a(n-6) -6644*a(n-7) -8872*a(n-8) +13920*a(n-9) +13824*a(n-10) -13056*a(n-11) -10688*a(n-12) +4288*a(n-13) +3072*a(n-14)

cp's OEIS Frontend

A220611 Number of ways to reciprocally link elements of an n X 5 array either to themselves or to exactly two horizontal and vertical neighbors, without consecutive collinear links.

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A220612 Number of ways to reciprocally link elements of an nX6 array either to themselves or to exactly two horizontal and vertical neighbors, without consecutive collinear links.

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A220613 Number of ways to reciprocally link elements of an nX7 array either to themselves or to exactly two horizontal and vertical neighbors, without consecutive collinear links.

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Examples

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