A220735 Number of ways to reciprocally link elements of an nX5 array either to themselves or to exactly two horizontal, diagonal and antidiagonal neighbors, without consecutive collinear links

1, 32, 487, 7369, 127288, 2027456, 32924133, 534490260, 8661108365, 140500900684, 2278575841968, 36953271570273, 599311228551359, 9719536107936096, 157630560274669449, 2556437605930905145, 41460052609326887864

Offset

1,2

Comments

Column 5 of A220738

Links

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

Formula

Empirical: a(n) = 20*a(n-1) -65*a(n-2) +76*a(n-3) -1155*a(n-4) +18496*a(n-5) -70044*a(n-6) +72160*a(n-7) -378281*a(n-8) +114092*a(n-9) -564419*a(n-10) +5536756*a(n-11) +25967998*a(n-12) +37954124*a(n-13) +153656513*a(n-14) -157832972*a(n-15) -745918733*a(n-16) -1917603040*a(n-17) -4791944316*a(n-18) -4163305184*a(n-19) +6977275361*a(n-20) +12706741652*a(n-21) +68686379451*a(n-22) +126029637644*a(n-23) +62729877905*a(n-24) +70631612552*a(n-25) -248226923306*a(n-26) -788443556936*a(n-27) -938536545342*a(n-28) -49553932544*a(n-29) -87300444152*a(n-30) -1751070963072*a(n-31) +510955338150*a(n-32) +939527443832*a(n-33) -3349453802910*a(n-34) +1498736584968*a(n-35) +21039268013924*a(n-36) +20041433993432*a(n-37) -10137555492606*a(n-38) -18609838530008*a(n-39) -7234616664154*a(n-40) +12641325810368*a(n-41) +18097001487592*a(n-42) +16535299789824*a(n-43) -21228216014110*a(n-44) -51010314661528*a(n-45) +18061117651606*a(n-46) +8391340051480*a(n-47) +1477654226577*a(n-48) +11274541552932*a(n-49) -9396242028357*a(n-50) +2653547189052*a(n-51) +207617013041*a(n-52) +480000531904*a(n-53) -705614349292*a(n-54) -266915818336*a(n-55) +295072852243*a(n-56) -49147133412*a(n-57) -23941964399*a(n-58) +1948544708*a(n-59) +3237483262*a(n-60) -370954468*a(n-61) +8530157*a(n-62) +24305060*a(n-63) -31080201*a(n-64) -6824672*a(n-65) +1946900*a(n-66) -75296*a(n-67) +108077*a(n-68) -13372*a(n-69) +1151*a(n-70) +28*a(n-71) -a(n-72)

Example

Some solutions for n=3 0=self 1=nw 3=ne 4=w 6=e 7=sw 9=se (reciprocal directions total 10)
.00.69.47.79.00...00.00.00.67.47...00.69.47.69.47...69.47.79.00.00
.00.39.13.67.14...69.47.39.39.00...00.36.14.39.17...39.13.67.14.00
.00.00.13.00.00...36.14.00.16.14...00.00.00.36.14...00.13.00.00.00

Crossrefs

Sequence in context: A091364 A208312 A138412 * A010948 A022627 A238534

Adjacent sequences: A220732 A220733 A220734 * A220736 A220737 A220738

Keyword

nonn

Author

R. H. Hardin Dec 18 2012

Status

approved