A205938 Number of (n+1) X 3 0..3 arrays with no 2 X 2 subblock having the number of clockwise edge increases equal to the number of counterclockwise edge increases in its adjacent leftward or upward neighbors.

1776, 11028, 81864, 620988, 4601832, 34647764, 258956760, 1942182832, 14548134360, 109048169588, 816513313600, 6119001144252, 45844697097568, 343491408375096, 2573223557463040, 19280035339388884, 144450083231226680

Offset

1,1

Comments

Column 2 of A205944.

Links

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

Formula

Empirical: a(n) = 20*a(n-2) +106*a(n-3) +1073*a(n-4) +1676*a(n-5) -3921*a(n-6) +2510*a(n-7) +10367*a(n-8) -39660*a(n-9) -93737*a(n-10) +67098*a(n-11) +1223861*a(n-12) -354734*a(n-13) -10343391*a(n-14) +12014472*a(n-15) +13924079*a(n-16) -59795244*a(n-17) +51740047*a(n-18) +57373456*a(n-19) -110979072*a(n-20) +74835622*a(n-21) -35991056*a(n-22) -22750738*a(n-23) +144074425*a(n-24) -153484616*a(n-25) +22971007*a(n-26) +78260016*a(n-27) -114414927*a(n-28) +63699940*a(n-29) +5571416*a(n-30) -148244590*a(n-31) +124206264*a(n-32) -55439888*a(n-33) -56510828*a(n-34) +78816744*a(n-35) -51200538*a(n-36) -18471918*a(n-37) +26953636*a(n-38) -21588268*a(n-39) -34226*a(n-40) +2404520*a(n-41) -4650695*a(n-42) -885160*a(n-43) -143680*a(n-44) -32966*a(n-45) -70777*a(n-46) -35254*a(n-47) +10119*a(n-48) +3744*a(n-49) -981*a(n-50) -4*a(n-51) for n>54.

Example

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

Crossrefs

Sequence in context: A185836 A047826 A143995 * A238307 A233953 A282404

Adjacent sequences: A205935 A205936 A205937 * A205939 A205940 A205941

Keyword

nonn

Author

R. H. Hardin, Feb 01 2012

Status

approved