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, 8, 72, 712, 7369, 78418, 824965, 8705465, 91846148, 969455702, 10232057400, 107999532301, 1139908791516, 12031592724549, 126991550832525, 1340378087066328, 14147494420206468, 149324775605316448

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