A231110 Number of 4Xn 0..3 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero

0, 0, 42, 438, 4674, 53530, 616562, 7084870, 81402688, 935286238, 10746062272, 123467810184, 1418593781388, 16299052416028, 187269334301006, 2151646785715718, 24721526971823592, 284040066485994938

Offset

1,3

Comments

Row 4 of A231108

Links

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

Formula

Empirical: a(n) = 28*a(n-1) -284*a(n-2) +1189*a(n-3) -144*a(n-4) -16202*a(n-5) +43314*a(n-6) +51726*a(n-7) -378092*a(n-8) +142812*a(n-9) +1787045*a(n-10) -2071922*a(n-11) -5399600*a(n-12) +10035017*a(n-13) +9756451*a(n-14) -27257530*a(n-15) -9262577*a(n-16) +43800387*a(n-17) +823484*a(n-18) -25963993*a(n-19) -5631788*a(n-20) -43551782*a(n-21) +58894906*a(n-22) +72195172*a(n-23) -73850308*a(n-24) +9275284*a(n-25) -85663152*a(n-26) -50216070*a(n-27) +247099342*a(n-28) -15789086*a(n-29) -168327877*a(n-30) +34428902*a(n-31) -8906080*a(n-32) +16412437*a(n-33) +62237635*a(n-34) -31892052*a(n-35) -25353207*a(n-36) +10821699*a(n-37) -31603*a(n-38) +689681*a(n-39) +2169758*a(n-40) -686435*a(n-41) -375254*a(n-42) -46338*a(n-43) -50759*a(n-44) +32108*a(n-45) +27901*a(n-46) +299*a(n-47) -4056*a(n-48) -595*a(n-49) +162*a(n-50) +48*a(n-51) for n>56

Example

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

Crossrefs

Sequence in context: A242144 A242145 A230933 * A156762 A248094 A244909

Adjacent sequences: A231107 A231108 A231109 * A231111 A231112 A231113

Keyword

nonn

Author

R. H. Hardin, Nov 03 2013

Status

approved