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

1,1

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)

Links

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

Formula

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

Example

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

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

Sequence in context: A094474 A064109 A175484 * A298316 A299190 A156682

Adjacent sequences: A210691 A210692 A210693 * A210695 A210696 A210697

Keyword

nonn,tabl

Author

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

Status

approved