A210694 T(n,k)=Number of (n+1)X(n+1) -k..k symmetric matrices with every 2X2 subblock having sum zero.

5, 13, 9, 25, 35, 17, 41, 91, 97, 33, 61, 189, 337, 275, 65, 85, 341, 881, 1267, 793, 129, 113, 559, 1921, 4149, 4825, 2315, 257, 145, 855, 3697, 10901, 19721, 18571, 6817, 513, 181, 1241, 6497, 24583, 62281, 94509, 72097, 20195, 1025, 221, 1729, 10657, 49575

Offset: 1

Author

R. H. Hardin, with R. J. Mathar in the Sequence Fans Mailing List, Mar 30 2012

Keywords

• nonn
• tabl

Comments

Table starts

...5....13.....25......41.......61.......85.......113.......145........181

...9....35.....91.....189......341......559.......855......1241.......1729

..17....97....337.....881.....1921.....3697......6497.....10657......16561

..33...275...1267....4149....10901....24583.....49575.....91817.....159049

..65...793...4825...19721....62281...164305....379793....793585....1531441

.129..2315..18571...94509...358061..1103479...2920695...6880121...14782969

.257..6817..72097..456161..2070241..7444417..22542017..59823937..143046721

.513.20195.281827.2215269.12030821.50431303.174571335.521638217.1387420489

Solutions are determined by the diagonal, extended with x(i,j) = (x(i,i)+x(j,j))/2 * (-1)^(i-j)

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..10000

Crossrefs

cf. A179927

Column 1 is A000051(n+1)

Column 2 is A007689(n+1)

Column 3 is A074605(n+1)

Column 4 is A074611(n+1)

Column 5 is A074615(n+1)

Column 6 is A074619(n+1)

Column 7 is A074622(n+1)

Column 8 is A074624(n+1)

Row 1 is A001844

Row 2 is A005898

Row 3 is A008514

Row 4 is A008515

Row 5 is A008516

Row 6 is A036085

Row 7 is A036086

Row 8 is A036087

Formula

T(n,k)=k^(n+1)+(k+1)^(n+1)