A198664 Number of nX3 0..4 arrays with values 0..4 introduced in row major order and each element equal to one or two horizontal and vertical neighbors

1, 13, 132, 2715, 59281, 1544783, 40546053, 1100262051, 29830418147, 813591963761, 22176955780999, 605153141144795, 16510148540966104, 450529856078844767, 12293523860930239681, 335463844113052677850

Offset

1,2

Comments

Column 3 of A198669

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 26*a(n-1) +207*a(n-2) -4693*a(n-3) -5776*a(n-4) +157591*a(n-5) +139443*a(n-6) -1825139*a(n-7) -3912555*a(n-8) +9205948*a(n-9) +49540346*a(n-10) -50523258*a(n-11) -187400427*a(n-12) +193241548*a(n-13) +457708054*a(n-14) -2348260717*a(n-15) -853094525*a(n-16) +19413615836*a(n-17) -4559327195*a(n-18) -81422778316*a(n-19) +29945338304*a(n-20) +301610165665*a(n-21) -167143208735*a(n-22) -816553663024*a(n-23) +863486594864*a(n-24) +360655337798*a(n-25) -4549562921429*a(n-26) +2936432568750*a(n-27) +19962871586477*a(n-28) -6710978972167*a(n-29) -45546401098564*a(n-30) +12779999633307*a(n-31) +41720387693559*a(n-32) -36287192385505*a(n-33) +1527013277477*a(n-34) +152317108173902*a(n-35) +35931632692232*a(n-36) -236911335057032*a(n-37) -134246505542044*a(n-38) -202262924273384*a(n-39) -284614527001184*a(n-40) +24380741738928*a(n-41) +465170070212768*a(n-42) +610398531322432*a(n-43) +205669857696256*a(n-44) +965878890074624*a(n-45) -10768073967104*a(n-46) +541791030492160*a(n-47) +1703742317537280*a(n-48) -974079293448192*a(n-49) -101946236010496*a(n-50) -762059395989504*a(n-51) -2488636072656896*a(n-52) -986411874910208*a(n-53) -226783416811520*a(n-54) -358318577025024*a(n-55) +403639919181824*a(n-56) +362849171931136*a(n-57) +64276333068288*a(n-58) -22574348107776*a(n-59) -14843406974976*a(n-60) for n>61

Example

Some solutions with all values 0 to 4 for n=4
..0..1..1....0..1..2....0..1..1....0..0..1....0..0..0....0..1..2....0..1..1
..0..2..2....0..1..2....0..2..2....2..2..1....1..2..2....0..1..2....0..0..2
..3..3..3....0..0..3....3..4..1....3..4..1....1..3..3....2..3..3....3..2..2
..4..4..4....4..4..3....3..4..1....3..4..1....4..4..4....2..4..4....3..4..4

Crossrefs

Sequence in context: A037617 A295603 A199144 * A332243 A081042 A329019

Adjacent sequences: A198661 A198662 A198663 * A198665 A198666 A198667

Keyword

nonn

Author

R. H. Hardin Oct 28 2011

Status

approved