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A235017 T(n,k) is the number of (n+1) X (k+1) 0..4 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 3, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings). 8
40, 104, 104, 264, 224, 264, 680, 488, 488, 680, 1736, 1112, 936, 1112, 1736, 4456, 2568, 1912, 1912, 2568, 4456, 11400, 6088, 4008, 3560, 4008, 6088, 11400, 29224, 14600, 8760, 6856, 6856, 8760, 14600, 29224, 74824, 35560, 19560, 13912, 12168 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

      40    104    264    680   1736   4456  11400   29224   74824  191720

     104    224    488   1112   2568   6088  14600   35560   87368  216680

     264    488    936   1912   4008   8760  19560   44952  105128  250744

     680   1112   1912   3560   6856  13912  28968   62600  138360  314376

    1736   2568   4008   6856  12168  23016  44680   90824  189032  407880

    4456   6088   8760  13912  23016  40968  74888  144184  283832  581720

   11400  14600  19560  28968  44680  74888 128776  235240  437928  853928

   29224  35560  44952  62600  90824 144184 235240  410760  729688 1363336

   74824  87368 105128 138360 189032 283832 437928  729688 1234216 2211128

  191720 216680 250744 314376 407880 581720 853928 1363336 2211128 3822728

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..480

FORMULA

Empirical for column k (the k=4..7 recurrence also works for k=1..3; apparently every row and column satisfies the same order 10 recurrence):

k=1: a(n) = a(n-1) +4*a(n-2).

k=2: a(n) = 3*a(n-1) +4*a(n-2) -14*a(n-3) -4*a(n-4) +16*a(n-5).

k=3: [order 8].

k=4..7: [same order 10 recurrence].

EXAMPLE

Some solutions for n=4, k=4:

  2 1 2 1 2      3 2 0 2 4      3 1 3 1 3      0 4 0 4 0

  0 2 0 2 0      1 3 4 3 2      2 3 2 3 2      2 3 2 3 2

  2 1 2 1 2      3 2 0 2 4      0 4 0 4 0      4 2 4 2 4

  4 0 4 0 4      1 3 4 3 2      2 3 2 3 2      0 1 0 1 0

  2 1 2 1 2      3 2 0 2 4      3 1 3 1 3      2 0 2 0 2

CROSSREFS

Column 1 is A185761(n+1).

Sequence in context: A235280 A235271 A033832 * A043219 A039396 A043999

Adjacent sequences:  A235014 A235015 A235016 * A235018 A235019 A235020

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 02 2014

STATUS

approved

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Last modified August 16 07:50 EDT 2022. Contains 356160 sequences. (Running on oeis4.)