A220688 -id:A220688 - cp's OEIS frontend

A220683 Number of ways to reciprocally link elements of an n X 3 array either to themselves or to exactly two horizontal, vertical or antidiagonal neighbors.

1, 12, 94, 745, 5851, 46027, 362057, 2847943, 22401961, 176214299, 1386105209, 10903131303, 85764249269, 674623302927, 5306600415489, 41741825175435, 328342033045001, 2582745009614887, 20315923985816277, 159805465061769263

Offset: 1

R. H. Hardin, Dec 17 2012

nonn

Column 3 of A220688.

			Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10):
.68.46.47...68.47.00...00.67.48...00.00.00...68.47.00...00.67.48...00.78.00
.28.36.48...23.67.47...36.47.27...68.46.47...23.67.48...38.68.24...38.26.48
.26.46.24...36.34.00...36.34.00...26.34.00...36.46.24...26.24.00...26.46.24

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

Cf. A220688.

Empirical: a(n) = 6*a(n-1) + 12*a(n-2) + 19*a(n-3) + 16*a(n-4) + 2*a(n-5) for n>6.

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

A220684 Number of ways to reciprocally link elements of an nX4 array either to themselves or to exactly two horizontal, vertical or antidiagonal neighbors.

Original entry on oeis.org

1, 37, 745, 15452, 312603, 6349886, 128995678, 2620320833, 53226950200, 1081210102382, 21962842195925, 446135673339403, 9062444632025696, 184087280486642815, 3739402357364779367, 75959240384539034764

Offset: 1

R. H. Hardin Dec 17 2012

nonn

Column 4 of A220688

			Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10)
.00.67.48.78...68.46.46.47...00.00.00.78...00.00.68.48...68.46.46.47
.38.78.23.27...26.48.37.00...00.67.34.27...00.68.24.27...28.00.38.00
.23.26.34.00...00.23.00.00...36.46.34.00...00.26.34.00...26.46.24.00

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

Empirical: a(n) = 15*a(n-1) +89*a(n-2) +365*a(n-3) +522*a(n-4) -1997*a(n-5) -10213*a(n-6) -23837*a(n-7) -26018*a(n-8) +7514*a(n-9) +19116*a(n-10) -3306*a(n-11) -5327*a(n-12) +2212*a(n-13) +316*a(n-14) -285*a(n-15) +12*a(n-17) -a(n-18)

A220685 Number of ways to reciprocally link elements of an nX5 array either to themselves or to exactly two horizontal, vertical or antidiagonal neighbors.

Original entry on oeis.org

1, 114, 5851, 312603, 15978924, 822649205, 42362190063, 2181341369109, 112319870453715, 5783510938076077, 297801401665428743, 15334225523450669062, 789581475759386788696, 40656693721278204870112

Offset: 1

R. H. Hardin Dec 17 2012

nonn

Column 5 of A220688

			Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10)
.00.78.68.48.78...00.67.46.46.48...00.00.00.68.48...00.78.68.47.00
.36.24.28.23.27...38.68.48.68.24...00.78.00.28.28...38.27.23.78.00
.00.00.26.34.00...26.24.26.24.00...36.24.00.26.24...23.00.36.24.00

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

Empirical: a(n) = 35*a(n-1) +673*a(n-2) +8237*a(n-3) +46927*a(n-4) -112480*a(n-5) -3992526*a(n-6) -35333024*a(n-7) -169366609*a(n-8) -361164394*a(n-9) +47195630*a(n-10) +13502054*a(n-11) +495005695*a(n-12) +6209070799*a(n-13) +5791334536*a(n-14) -11945755468*a(n-15) -10812604841*a(n-16) +3004142790*a(n-17) -8986269878*a(n-18) +26749603735*a(n-19) -17268218707*a(n-20) +10625240169*a(n-21) +1286966410*a(n-22) -5196232889*a(n-23) -236330168*a(n-24) +3747662678*a(n-25) -4565014033*a(n-26) +2769440835*a(n-27) -1086425818*a(n-28) +220144889*a(n-29) -12788683*a(n-30) -5653764*a(n-31) +2046130*a(n-32) -331034*a(n-33) +12027*a(n-34) +3632*a(n-35) +36*a(n-36) for n>37

A220686 Number of ways to reciprocally link elements of an nX6 array either to themselves or to exactly two horizontal, vertical or antidiagonal neighbors.

Original entry on oeis.org

1, 351, 46027, 6349886, 822649205, 107713940118, 14108684022136, 1848014307847883, 242044667782801540, 31702119421997470360, 4152232349834304063419, 543844751860183504221026

Offset: 1

R. H. Hardin Dec 17 2012

nonn

Column 6 of A220688

			Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10)
.00.67.46.46.46.48...00.00.68.48.00.00...00.67.46.46.46.48...68.46.47.68.46.48
.38.67.46.47.78.28...00.00.26.24.68.47...36.46.47.00.67.24...26.34.00.26.48.27
.23.00.36.34.26.24...00.00.00.00.23.00...00.36.46.34.00.00...00.00.00.00.23.00

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

A220687 Number of ways to reciprocally link elements of an nX7 array either to themselves or to exactly two horizontal, vertical or antidiagonal neighbors.

Original entry on oeis.org

1, 1081, 362057, 128995678, 42362190063, 14108684022136, 4701615485821782, 1566852499542855296, 522108399243273023731, 173978947909208417520148, 57974051497341052095013087, 19318375776055542860988503113

Offset: 1

R. H. Hardin Dec 17 2012

nonn

Column 7 of A220688

			Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10)
.00.00.67.46.46.47.00...00.00.00.00.68.48.00...00.00.68.48.68.46.48
.00.36.46.47.37.67.47...00.67.48.00.27.26.47...00.78.28.28.26.47.28
.00.00.36.34.36.34.00...36.46.24.36.46.34.00...36.24.26.24.36.46.24

R. H. Hardin, Table of n, a(n) for n = 1..114

A220682 Number of ways to reciprocally link elements of an n X n array either to themselves or to exactly two horizontal, vertical or antidiagonal neighbors.

Original entry on oeis.org

1, 4, 94, 15452, 15978924, 107713940118, 4701615485821782, 1328565529272722924682, 2429341045430456043662317796

Offset: 1

R. H. Hardin Dec 17 2012

nonn

Diagonal of A220688

			Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10)
.68.48.78...00.68.48...00.00.00...00.00.78...00.67.48...68.47.78...00.68.48
.28.23.28...00.26.24...00.78.00...00.36.24...38.00.27...23.37.28...68.24.28
.26.46.24...00.00.00...36.24.00...00.00.00...26.34.00...36.46.24...26.46.24

cp's OEIS Frontend

A220683 Number of ways to reciprocally link elements of an n X 3 array either to themselves or to exactly two horizontal, vertical or antidiagonal neighbors.

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A220684 Number of ways to reciprocally link elements of an nX4 array either to themselves or to exactly two horizontal, vertical or antidiagonal neighbors.

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A220685 Number of ways to reciprocally link elements of an nX5 array either to themselves or to exactly two horizontal, vertical or antidiagonal neighbors.

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A220686 Number of ways to reciprocally link elements of an nX6 array either to themselves or to exactly two horizontal, vertical or antidiagonal neighbors.

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A220687 Number of ways to reciprocally link elements of an nX7 array either to themselves or to exactly two horizontal, vertical or antidiagonal neighbors.

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A220682 Number of ways to reciprocally link elements of an n X n array either to themselves or to exactly two horizontal, vertical or antidiagonal neighbors.

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