A211470 Number of (n+1)X(n+1) -8..8 symmetric matrices with every 2X2 subblock having sum zero and one, two or three distinct values

145, 397, 945, 2153, 4775, 10527, 22995, 50565, 110915, 245927, 545909, 1225707, 2760503, 6282475, 14352999, 33082005, 76545031, 178364381, 417062331, 980496727, 2311774857, 5472654325, 12985260305, 30901798587, 73669894089

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) +14*a(n-2) -144*a(n-3) -12*a(n-4) +1553*a(n-5) -1086*a(n-6) -9957*a(n-7) +11142*a(n-8) +42330*a(n-9) -59054*a(n-10) -126094*a(n-11) +201376*a(n-12) +271448*a(n-13) -474492*a(n-14) -430008*a(n-15) +794866*a(n-16) +506763*a(n-17) -953966*a(n-18) -447303*a(n-19) +814746*a(n-20) +296554*a(n-21) -485322*a(n-22) -146850*a(n-23) +194433*a(n-24) +52926*a(n-25) -49234*a(n-26) -13004*a(n-27) +7010*a(n-28) +1900*a(n-29) -420*a(n-30) -120*a(n-31)

Example

Some solutions for n=3
.-1.-1.-1..4....2..0..0.-2....2.-2..2.-2...-2..1.-2..0....3.-2..1.-1
.-1..3.-1.-2....0.-2..2..0...-2..2.-2..2....1..0..1..1...-2..1..0..0
.-1.-1.-1..4....0..2.-2..0....2.-2..2.-2...-2..1.-2..0....1..0.-1..1
..4.-2..4.-7...-2..0..0..2...-2..2.-2..2....0..1..0..2...-1..0..1.-1

Crossrefs

Sequence in context: A094613 A207058 A116208 * A031702 A297732 A354669

Adjacent sequences: A211467 A211468 A211469 * A211471 A211472 A211473

Keyword

nonn

Author

R. H. Hardin Apr 12 2012

Status

approved