A205654 Number of (n+1)X4 0..3 arrays with every 2 X 2 subblock having the same number of clockwise edge increases as its horizontal neighbors and no 2 X 2 subblock having the same number of counterclockwise edge increases as its vertical neighbors.

15616, 95008, 511632, 3227968, 21711080, 142040528, 939384668, 6315887616, 43127525028, 293504124464, 2010761042684, 13765588024992, 94808427226252, 651171548709344, 4492250394556948, 30900830935136448, 213414348556901300

Offset

1,1

Comments

Column 3 of A205659.

Links

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

Formula

Empirical: a(n) = 123*a(n-2) -5628*a(n-4) +148*a(n-5) +116088*a(n-6) -16012*a(n-7) -759206*a(n-8) +691292*a(n-9) -12017217*a(n-10) -15889892*a(n-11) +280873558*a(n-12) +215169248*a(n-13) -2200690341*a(n-14) -1751686412*a(n-15) +4583289563*a(n-16) +7742440744*a(n-17) +49442254890*a(n-18) -3958925736*a(n-19) -446172389405*a(n-20) -186200780620*a(n-21) +1524636536309*a(n-22) +1405395261164*a(n-23) -725819718225*a(n-24) -6088979455296*a(n-25) -16586935486022*a(n-26) +18799040541752*a(n-27) +88923716370883*a(n-28) -44650025794612*a(n-29) -275338133098336*a(n-30) +84816752203836*a(n-31) +618137859409207*a(n-32) -131416583699744*a(n-33) -1079708701420623*a(n-34) +166875575325188*a(n-35) +1502288232779585*a(n-36) -171522340603780*a(n-37) -1654174438614734*a(n-38) +135930301455756*a(n-39) +1366322441174106*a(n-40) -67948082220432*a(n-41) -663033247947406*a(n-42) -12335897290212*a(n-43) -228162624499636*a(n-44) +85841864206000*a(n-45) +1013390893024203*a(n-46) -143989548233328*a(n-47) -1514615583335587*a(n-48) +185064001530040*a(n-49) +1727367950741340*a(n-50) -203853632634644*a(n-51) -1716417117600201*a(n-52) +190684118816484*a(n-53) +1509134660213129*a(n-54) -142294398019888*a(n-55) -1104312799492165*a(n-56) +70860823023280*a(n-57) +547935024501374*a(n-58) -537789934620*a(n-59) +24017490573989*a(n-60) -46208705709452*a(n-61) -437509068236846*a(n-62) +61155341457296*a(n-63) +592258860492842*a(n-64) -51855547665328*a(n-65) -520811261472978*a(n-66) +32976685435752*a(n-67) +343103177446545*a(n-68) -16275942966264*a(n-69) -174587800161488*a(n-70) +6238262983124*a(n-71) +68570740598522*a(n-72) -1834097494060*a(n-73) -20529485948585*a(n-74) +407837207740*a(n-75) +4620423229974*a(n-76) -68747714752*a(n-77) -783563489744*a(n-78) +9331942944*a(n-79) +106462224784*a(n-80) -1170002336*a(n-81) -13373480224*a(n-82) +138491712*a(n-83) +1597556784*a(n-84) -11929920*a(n-85) -139247136*a(n-86) +483840*a(n-87) +5703936*a(n-88) for n>95.

Example

Some solutions for n=4:
..0..1..1..2....3..0..3..1....2..3..3..2....1..2..3..2....0..2..1..3
..2..3..2..3....1..3..2..1....3..1..0..3....3..1..2..0....0..2..1..2
..2..1..0..3....1..3..2..3....3..3..3..3....3..1..2..0....1..0..3..2
..3..1..1..1....0..1..0..3....3..3..3..3....1..0..1..2....0..0..0..0
..3..3..0..1....0..0..0..1....0..0..0..2....0..0..1..1....1..2..3..3

Crossrefs

Sequence in context: A247692 A262793 A206104 * A206183 A205365 A254029

Adjacent sequences: A205651 A205652 A205653 * A205655 A205656 A205657

Keyword

nonn

Author

R. H. Hardin, Jan 30 2012

Status

approved