A196333 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,3,1,2 for x=0,1,2,3,4

5, 17, 50, 335, 894, 3246, 14973, 64423, 270901, 1067992, 4278465, 17554846, 73250696, 303360883, 1240601669, 5071382869, 20820082942, 85773230271, 353226448334, 1451624154342, 5960878160915, 24492093845487, 100710579314169

Offset

1,1

Comments

Every 0 is next to 0 4's, every 1 is next to 1 0's, every 2 is next to 2 3's, every 3 is next to 3 1's, every 4 is next to 4 2's

Column 4 of A196337

Links

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

Formula

Empirical: a(n) = 5*a(n-1) -4*a(n-2) +26*a(n-4) +56*a(n-5) -358*a(n-6) -748*a(n-7) -896*a(n-8) +909*a(n-9) +187*a(n-10) -12078*a(n-11) +42445*a(n-12) +97050*a(n-13) +246286*a(n-14) +522734*a(n-15) +662122*a(n-16) -574583*a(n-17) -2576076*a(n-18) -7793975*a(n-19) -18081736*a(n-20) -11777431*a(n-21) -37101001*a(n-22) -40924777*a(n-23) +19988497*a(n-24) +20268565*a(n-25) +59783847*a(n-26) +29293979*a(n-27) +59333365*a(n-28) -2116548*a(n-29) -34111094*a(n-30) -18558798*a(n-31) -28606287*a(n-32) -8559806*a(n-33) -18722495*a(n-34) +1768049*a(n-35) +8214636*a(n-36) +12355852*a(n-37) +15376*a(n-38) +6620070*a(n-39) +393935*a(n-40) +4096014*a(n-41) -2372022*a(n-42) +503938*a(n-43) -494622*a(n-44) -65073*a(n-45) -85243*a(n-46) -185276*a(n-47) +85167*a(n-48) -25581*a(n-49) +7530*a(n-50) +4334*a(n-51) -193*a(n-52) +967*a(n-53) -255*a(n-54)

Example

Some solutions for n=5
..1..0..0..1....0..0..0..0....1..0..0..1....1..1..1..1....1..0..0..1
..1..0..0..1....0..0..0..0....1..0..0..1....0..0..0..0....1..3..1..1
..1..1..3..1....1..3..1..1....3..1..1..3....1..1..1..1....0..1..3..0
..0..1..1..0....3..1..1..3....1..3..3..1....3..1..1..1....0..3..1..0
..1..3..1..0....1..0..0..1....0..1..1..0....1..0..0..0....0..1..3..1

Crossrefs

Sequence in context: A054452 A196310 A196283 * A039783 A374185 A103685

Adjacent sequences: A196330 A196331 A196332 * A196334 A196335 A196336

Keyword

nonn

Author

R. H. Hardin Oct 01 2011

Status

approved