A211816 Number of (n+1)X(n+1) -10..10 symmetric matrices with every 2X2 subblock having sum zero and two or three distinct values

220, 602, 1368, 2942, 6088, 12442, 24924, 50194, 99390, 199570, 394162, 793028, 1569220, 3170790, 6300354, 12799142, 25565534, 52235044, 104925530, 215604840, 435513812, 899750556, 1827061522, 3793414420, 7740115362, 16142443314

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..210

Formula

Empirical: a(n) = 6*a(n-1) +16*a(n-2) -160*a(n-3) -15*a(n-4) +1883*a(n-5) -1614*a(n-6) -12827*a(n-7) +18643*a(n-8) +55534*a(n-9) -110733*a(n-10) -156457*a(n-11) +420605*a(n-12) +273571*a(n-13) -1096609*a(n-14) -220702*a(n-15) +2018897*a(n-16) -191679*a(n-17) -2645653*a(n-18) +814093*a(n-19) +2453538*a(n-20) -1164914*a(n-21) -1580007*a(n-22) +985631*a(n-23) +680255*a(n-24) -535843*a(n-25) -180672*a(n-26) +188098*a(n-27) +23218*a(n-28) -41026*a(n-29) +676*a(n-30) +5032*a(n-31) -568*a(n-32) -264*a(n-33) +48*a(n-34)

Example

Some solutions for n=3
.-1..3.-1.-1....6.-2..4.-2...-3.-3.-3..0...-1..2.-1..2....2..1..1..1
..3.-5..3.-1...-2.-2..0.-2...-3..9.-3..6....2.-3..2.-3....1.-4..2.-4
.-1..3.-1.-1....4..0..2..0...-3.-3.-3..0...-1..2.-1..2....1..2..0..2
.-1.-1.-1..3...-2.-2..0.-2....0..6..0..3....2.-3..2.-3....1.-4..2.-4

Crossrefs

Sequence in context: A260203 A184543 A234558 * A135807 A258545 A257361

Adjacent sequences: A211813 A211814 A211815 * A211817 A211818 A211819

Keyword

nonn

Author

R. H. Hardin Apr 21 2012

Status

approved