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

1,1

Comments

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

Links

R. H. Hardin, Table of n, a(n) for n = 1..760

Jon Maiga, Computer-generated formulas for A204713, Sequence Machine.

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)

Example

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

Crossrefs

Column 1 is A004119(n+1).

Cf. A183688.

Sequence in context: A352352 A090229 A259222 * A241985 A194408 A376298

Adjacent sequences: A204710 A204711 A204712 * A204714 A204715 A204716

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 18 2012

Status

approved