A196926 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 1,4,3,2,0 for x=0,1,2,3,4

1, 1, 5, 17, 65, 231, 833, 3023, 10988, 39907, 144974, 526573, 1912811, 6948283, 25239895, 91684511, 333046794, 1209801776, 4394640748, 15963659925, 57988462172, 210644781240, 765173326354, 2779514464213, 10096667528545

Offset

1,3

Comments

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

Column 5 of A196929

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +8*a(n-2) -4*a(n-3) -9*a(n-4) -6*a(n-5) +8*a(n-6) -82*a(n-7) -168*a(n-8) -19*a(n-9) -269*a(n-10) +355*a(n-11) +880*a(n-12) +1079*a(n-13) +2013*a(n-14) +823*a(n-15) +1049*a(n-16) -3153*a(n-17) -4163*a(n-18) -6020*a(n-19) -9104*a(n-20) -2739*a(n-21) -5044*a(n-22) +5777*a(n-23) +4722*a(n-24) +8719*a(n-25) +11564*a(n-26) +1018*a(n-27) +7836*a(n-28) -3176*a(n-29) -2803*a(n-30) -2290*a(n-31) -5139*a(n-32) -1811*a(n-33) -2804*a(n-34) -347*a(n-35) -1423*a(n-36) +1064*a(n-37) +576*a(n-38) +762*a(n-39) +1627*a(n-40) -104*a(n-41) +466*a(n-42) -168*a(n-43) -374*a(n-44) -112*a(n-46) +24*a(n-48)

Example

Some solutions for n=4
..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
..0..0..0..0..0....0..4..0..0..0....0..0..0..0..0....0..4..0..4..0
..0..0..0..4..0....0..0..0..0..0....0..4..0..0..0....0..0..4..0..0
..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0

Crossrefs

Sequence in context: A273483 A253067 A273793 * A120893 A195531 A273535

Adjacent sequences: A196923 A196924 A196925 * A196927 A196928 A196929

Keyword

nonn

Author

R. H. Hardin Oct 07 2011

Status

approved