A220602 -id:A220602 - cp's OEIS frontend

A220597 Number of ways to reciprocally link elements of an n X 3 array either to themselves or to exactly two horizontal, vertical and antidiagonal neighbors, without 3-loops.

1, 7, 65, 471, 3469, 25747, 190425, 1408823, 10424813, 77135267, 570740149, 4223043591, 31247282909, 231205914319, 1710746473929, 12658211881263, 93661059763965, 693020010391803, 5127816575062977, 37941909947454471

Offset: 1

R. H. Hardin, Dec 16 2012

nonn

Column 3 of A220602.

			Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10):
.68.46.48...00.67.47...00.68.48...00.68.48...00.67.47...68.46.47...00.00.78
.28.68.24...38.36.48...68.24.27...00.27.28...38.38.00...26.34.00...68.34.28
.26.24.00...26.46.24...26.34.00...36.46.24...26.24.00...00.00.00...26.46.24

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

Cf. A220602.

Empirical: a(n) = 6*a(n-1) + 7*a(n-2) + 25*a(n-3) - 3*a(n-4) + 9*a(n-5) + 22*a(n-6) - 5*a(n-7) - 2*a(n-8).

Empirical g.f.: x*(1 + x + 16*x^2 + 7*x^3 + 16*x^4 + 23*x^5 - 5*x^6 - 2*x^7) / ((1 - x + x^2)*(1 - 5*x - 13*x^2 - 33*x^3 - 17*x^4 + 7*x^5 + 2*x^6)). - Colin Barker, Aug 01 2018

A220598 Number of ways to reciprocally link elements of an nX4 array either to themselves or to exactly two horizontal, vertical and antidiagonal neighbors, without 3-loops.

Original entry on oeis.org

1, 17, 471, 9047, 167614, 3174778, 60138423, 1137615308, 21523535122, 407249783145, 7705461280893, 145792738613760, 2758505816300670, 52192947928719778, 987528662199324496, 18684763495713245969

Offset: 1

R. H. Hardin Dec 16 2012

nonn

Column 4 of A220602

			Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10)
.00.68.46.48...68.48.67.47...00.67.46.48...68.48.00.78...00.68.48.78
.00.27.00.28...28.23.36.48...38.67.47.28...26.24.37.28...00.27.23.28
.36.46.46.24...26.46.46.24...23.36.46.24...00.36.46.24...36.46.46.24

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

Empirical: a(n) = 15*a(n-1) +41*a(n-2) +606*a(n-3) +405*a(n-4) +679*a(n-5) -8407*a(n-6) -28555*a(n-7) +17039*a(n-8) +147483*a(n-9) +79534*a(n-10) -260454*a(n-11) -334003*a(n-12) +79493*a(n-13) +384190*a(n-14) +187418*a(n-15) -93878*a(n-16) -122508*a(n-17) -48185*a(n-18) -5142*a(n-19) +3204*a(n-20) +1023*a(n-21) +22*a(n-22) -9*a(n-23) -11*a(n-24) +a(n-25)

A220599 Number of ways to reciprocally link elements of an nX5 array either to themselves or to exactly two horizontal, vertical and antidiagonal neighbors, without 3-loops.

Original entry on oeis.org

1, 44, 3469, 167614, 7558495, 352586943, 16505365334, 770615995060, 35978245868462, 1680090131446571, 78453960278374893, 3663456651896335065, 171068067072237399646, 7988166245960912052019, 373013938796405801398629

Offset: 1

R. H. Hardin Dec 16 2012

nonn

Column 5 of A220602

			Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10)
.00.67.46.48.00...00.78.68.46.47...68.48.68.48.00...00.68.48.67.48
.38.00.67.24.00...38.27.27.36.47...28.28.28.28.00...00.27.23.67.24
.26.34.00.00.00...23.36.46.34.00...26.24.26.24.00...36.46.34.00.00

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

Empirical: a(n) = 35*a(n-1) +272*a(n-2) +11994*a(n-3) +32896*a(n-4) +309375*a(n-5) -3315691*a(n-6) -30948895*a(n-7) +48954898*a(n-8) -303997468*a(n-9) -7054837583*a(n-10) +8970311702*a(n-11) +269208688675*a(n-12) +485473331607*a(n-13) -3325199930663*a(n-14) -12213275584466*a(n-15) +11311850155580*a(n-16) +90662524191083*a(n-17) +29640254006904*a(n-18) -171828097518485*a(n-19) -32539810960422*a(n-20) -260809904785074*a(n-21) -1037755295924050*a(n-22) +553074708665462*a(n-23) -932747145758344*a(n-24) +248650789049878*a(n-25) -2856020100608967*a(n-26) +2696048261973157*a(n-27) -11016912810502883*a(n-28) -5911302056186341*a(n-29) -5797765198888052*a(n-30) +2541001897271391*a(n-31) -10148136754490004*a(n-32) -3988488395563961*a(n-33) +1004749709024694*a(n-34) -2533119314782758*a(n-35) -686156967660631*a(n-36) -1408624723023117*a(n-37) -377816092283658*a(n-38) +1379263668015862*a(n-39) -377091489287888*a(n-40) +120261293265251*a(n-41) +55405553060124*a(n-42) +82537043808782*a(n-43) +34671368481870*a(n-44) -25343134847072*a(n-45) +5386072841942*a(n-46) +8703786206652*a(n-47) -4039895276276*a(n-48) -181761484032*a(n-49) +98622190896*a(n-50) -183111581472*a(n-51) +38324067200*a(n-52) -13820570688*a(n-53) +313286432*a(n-54) +186406848*a(n-55) -3648192*a(n-56) +34560*a(n-57) -27648*a(n-58)

A220600 Number of ways to reciprocally link elements of an nX6 array either to themselves or to exactly two horizontal, vertical and antidiagonal neighbors, without 3-loops.

Original entry on oeis.org

1, 117, 25747, 3174778, 352586943, 41011388731, 4807269151250, 561355035745825, 65523075831128720, 7650441027984730028, 893266330737712903338, 104295209452828358545715, 12177239947634323813819907

Offset: 1

R. H. Hardin Dec 16 2012

nonn

Column 6 of A220602

			Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10)
.00.78.00.67.46.47...00.78.78.78.78.00...00.78.78.00.78.78...00.00.68.48.00.00
.38.26.34.78.38.00...38.23.23.23.26.47...38.23.27.37.23.28...68.48.26.24.67.47
.26.46.34.26.24.00...26.46.46.46.34.00...26.34.36.46.46.24...26.24.00.36.34.00

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

A220601 Number of ways to reciprocally link elements of an nX7 array either to themselves or to exactly two horizontal, vertical and antidiagonal neighbors, without 3-loops.

Original entry on oeis.org

1, 305, 190425, 60138423, 16505365334, 4807269151250, 1417058414112748, 415538772723268712, 121740835171119793585, 35681922955520577801844, 10458840906159008629586152, 3065510523366853897987776536

Offset: 1

R. H. Hardin Dec 16 2012

nonn

Column 7 of A220602

			Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10)
.00.00.00.00.00.00.78...00.67.48.68.48.00.78...00.78.00.00.67.46.48
.00.00.00.68.46.34.28...36.48.27.28.26.34.27...38.28.00.38.78.78.28
.00.00.00.26.46.46.24...00.23.00.26.46.34.00...26.24.00.23.23.26.24

R. H. Hardin, Table of n, a(n) for n = 1..116

A220596 Number of ways to reciprocally link elements of an n X n array either to themselves or to exactly two horizontal, vertical and antidiagonal neighbors, without 3-loops.

Original entry on oeis.org

1, 2, 65, 9047, 7558495, 41011388731, 1417058414112748, 305516864725171735943, 412489181606705015322075070

Offset: 1

R. H. Hardin Dec 16 2012

nonn

Diagonal of A220602

			Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10)
.00.00.00...00.78.78...68.46.47...68.46.48...00.67.48...00.78.00...00.67.47
.00.67.47...38.23.28...28.36.47...28.68.24...38.67.24...38.28.00...38.37.00
.36.34.00...26.46.24...26.34.00...26.24.00...23.00.00...26.24.00...23.00.00

cp's OEIS Frontend

A220597 Number of ways to reciprocally link elements of an n X 3 array either to themselves or to exactly two horizontal, vertical and antidiagonal neighbors, without 3-loops.

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A220598 Number of ways to reciprocally link elements of an nX4 array either to themselves or to exactly two horizontal, vertical and antidiagonal neighbors, without 3-loops.

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A220599 Number of ways to reciprocally link elements of an nX5 array either to themselves or to exactly two horizontal, vertical and antidiagonal neighbors, without 3-loops.

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A220600 Number of ways to reciprocally link elements of an nX6 array either to themselves or to exactly two horizontal, vertical and antidiagonal neighbors, without 3-loops.

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A220601 Number of ways to reciprocally link elements of an nX7 array either to themselves or to exactly two horizontal, vertical and antidiagonal neighbors, without 3-loops.

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A220596 Number of ways to reciprocally link elements of an n X n array either to themselves or to exactly two horizontal, vertical and antidiagonal neighbors, without 3-loops.

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