A204713 T(n,k) is the number of (n+1) X (k+1) 0..1 arrays with the permanents of all 2 X 2 subblocks equal and nonzero.

7, 13, 13, 25, 33, 25, 49, 81, 81, 49, 97, 209, 257, 209, 97, 193, 529, 833, 833, 529, 193, 385, 1361, 2689, 3473, 2689, 1361, 385, 769, 3473, 8705, 14145, 14145, 8705, 3473, 769, 1537, 8913, 28161, 58449, 73345, 58449, 28161, 8913, 1537, 3073, 22801, 91137

Offset: 1

Author

R. H. Hardin, Jan 18 2012

Keywords

• nonn
• tabl

Comments

This is A183688+1 (the +1 comes from the all-1 matrix). [Discovered by Sequence Machine] - Andrey Zabolotskiy, Oct 19 2021

Examples

			Table starts
    7   13    25     49       97       193        385         769         1537
   13   33    81    209      529      1361       3473        8913        22801
   25   81   257    833     2689      8705      28161       91137       294913
   49  209   833   3473    14145     58449     239425      986129      4047681
   97  529  2689  14145    73345    382849    1992321    10382977     54072961
  193 1361  8705  58449   382849   2542369   16748161   110871041    731709057
  385 3473 28161 239425  1992321  16748161  140090241  1174759297   9838208513
  769 8913 91137 986129 10382977 110871041 1174759297 12503757969 132720731393
Some solutions for n=4 k=3
  1  1  1  1    1  1  1  1    0  1  1  1    1  1  1  1    0  1  0  1
  0  1  0  1    0  1  0  1    1  0  1  0    0  1  0  1    1  1  1  0
  1  1  1  0    1  0  1  0    1  1  1  1    1  1  1  0    1  0  1  1
  0  1  0  1    1  1  0  1    0  1  0  1    1  0  1  1    0  1  1  0
  1  1  1  0    0  1  1  0    1  1  1  0    1  1  0  1    1  1  0  1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..760
• Jon Maiga, Computer-generated formulas for A204713, Sequence Machine.

Crossrefs

Column 1 is A004119(n+1).

Cf. A183688.

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-1) -2*a(n-2)

k=2: a(n) = 2*a(n-1) +3*a(n-2) -4*a(n-3)

k=3: a(n) = 3*a(n-1) +2*a(n-2) -4*a(n-3)

k=4: a(n) = a(n-1) +13*a(n-2) +3*a(n-3) -16*a(n-4)

k=5: a(n) = 4*a(n-1) +15*a(n-2) -38*a(n-3) -52*a(n-4) +72*a(n-5)

k=6: (order 9 recurrence)

k=7: (order 10 recurrence)