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A220741 Number of ways to reciprocally link elements of an 4Xn array either to themselves or to exactly two horizontal, diagonal and antidiagonal neighbors, without consecutive collinear links 1
1, 8, 72, 712, 7369, 78418, 824965, 8705465, 91846148, 969455702, 10232057400, 107999532301, 1139908791516, 12031592724549, 126991550832525, 1340378087066328, 14147494420206468, 149324775605316448 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row 4 of A220738

LINKS

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

FORMULA

Empirical: a(n) = 12*a(n-1) +21*a(n-2) -448*a(n-3) +279*a(n-4) +5524*a(n-5) -10795*a(n-6) -33243*a(n-7) +151603*a(n-8) +217375*a(n-9) -1696599*a(n-10) -2454563*a(n-11) +15287591*a(n-12) +25136093*a(n-13) -101932808*a(n-14) -160407951*a(n-15) +499186392*a(n-16) +576465951*a(n-17) -2102830964*a(n-18) -969873923*a(n-19) +8838550914*a(n-20) -1328714164*a(n-21) -27726463344*a(n-22) +6305121836*a(n-23) +56332035104*a(n-24) +3387670512*a(n-25) -97938123728*a(n-26) -15194857792*a(n-27) +250308293976*a(n-28) -43804316224*a(n-29) -804647616848*a(n-30) +134715853632*a(n-31) +2064903100288*a(n-32) -426059856960*a(n-33) -2947500723136*a(n-34) +659182787008*a(n-35) +2410402240064*a(n-36) -258105063808*a(n-37) -3557798438272*a(n-38) +3304226855808*a(n-39) +3630421527936*a(n-40) -5977152573952*a(n-41) -1282496314368*a(n-42) +1346378819328*a(n-43) +2095543107584*a(n-44) +1926031011328*a(n-45) +3765578029056*a(n-46) -6877547426816*a(n-47) -9325572079616*a(n-48) +4978969147392*a(n-49) +1690974281728*a(n-50) +9106783870976*a(n-51) +31327471878144*a(n-52) -13866806517760*a(n-53) -95837904863232*a(n-54) -11156622491648*a(n-55) +155368601485312*a(n-56) +68196053647360*a(n-57) -169300596883456*a(n-58) -117234867306496*a(n-59) +133558446850048*a(n-60) +112540616228864*a(n-61) -74271306022912*a(n-62) -65445707644928*a(n-63) +28342273179648*a(n-64) +17790281973760*a(n-65) -10585756401664*a(n-66) +10185609314304*a(n-67) +3751045758976*a(n-68) -14713727483904*a(n-69) -450006876160*a(n-70) +8988678684672*a(n-71) -278904438784*a(n-72) -3423156043776*a(n-73) +178509578240*a(n-74) +604516646912*a(n-75) -39191576576*a(n-76) -57982058496*a(n-77) +38654705664*a(n-78)

EXAMPLE

Some solutions for n=3 0=self 1=nw 3=ne 4=w 6=e 7=sw 9=se (reciprocal directions total 10)

.00.00.00...00.69.47...69.49.00...00.79.00...00.79.00...00.69.47...69.49.00

.00.00.00...00.39.17...00.16.14...36.49.17...39.79.17...00.36.14...00.17.17

.00.00.00...00.36.14...00.00.00...69.34.17...39.13.17...00.67.47...39.36.47

.00.00.00...00.00.00...00.00.00...00.13.00...00.13.00...36.34.00...00.13.00

CROSSREFS

Sequence in context: A082414 A145303 A098411 * A165323 A082366 A221159

Adjacent sequences:  A220738 A220739 A220740 * A220742 A220743 A220744

KEYWORD

nonn

AUTHOR

R. H. Hardin Dec 18 2012

STATUS

approved

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Last modified September 15 16:42 EDT 2019. Contains 327078 sequences. (Running on oeis4.)