A211336 - OEIS

A211336

Number of (n+1)X(n+1) -5..5 symmetric matrices with every 2X2 subblock having sum zero and two, three or four distinct values

60, 332, 1846, 10332, 58164, 329130, 1870664, 10670876, 61044918, 349974788, 2009495068, 11549465226, 66414142512, 381959562756, 2196335839046, 12624063953180, 72516570941316, 416247502883594, 2387248114517560

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OFFSET

1,1

COMMENTS

Symmetry and 2X2 block sums zero implies that the diagonal x(i,i) are equal modulo 2 and x(i,j)=(x(i,i)+x(j,j))/2*(-1)^(i-j)

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..74

FORMULA

Empirical: a(n) = 32*a(n-1) -429*a(n-2) +3078*a(n-3) -12340*a(n-4) +24890*a(n-5) -10895*a(n-6) -35870*a(n-7) +19131*a(n-8) +40338*a(n-9) +18694*a(n-10) +3532*a(n-11) +240*a(n-12)

EXAMPLE

Some solutions for n=3

.-3..1.-1..2....5.-3..0.-4....5.-2..4.-5....2..0.-1.-2....2.-1.-1..1

..1..1.-1..0...-3..1..2..2...-2.-1.-1..2....0.-2..3..0...-1..0..2.-2

.-1.-1..1..0....0..2.-5..1....4.-1..3.-4...-1..3.-4..1...-1..2.-4..4

..2..0..0.-1...-4..2..1..3...-5..2.-4..5...-2..0..1..2....1.-2..4.-4

CROSSREFS

Sequence in context: A096363 A033591 A133118 * A092478 A228889 A262385

Adjacent sequences: A211333 A211334 A211335 * A211337 A211338 A211339

KEYWORD

nonn

AUTHOR

R. H. Hardin Apr 07 2012

STATUS

approved