A211259 Number of (n+1)X(n+1) -6..6 symmetric matrices with every 2X2 subblock having sum zero and one, three or four distinct values

65, 335, 1703, 8645, 43643, 219333, 1097247, 5465297, 27114351, 134027929, 660336579, 3243840829, 15893481911, 77692754369, 379020868055, 1845782118641, 8974924575259, 43581782793301, 211388981838455, 1024316233634281

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) = 28*a(n-1) -155*a(n-2) -2658*a(n-3) +32061*a(n-4) +66366*a(n-5) -2314922*a(n-6) +3159336*a(n-7) +97801748*a(n-8) -317172988*a(n-9) -2797365748*a(n-10) +13347627288*a(n-11) +57922813108*a(n-12) -369288318800*a(n-13) -900259137962*a(n-14) +7525220569156*a(n-15) +10736644664141*a(n-16) -118794611594160*a(n-17) -100177501866905*a(n-18) +1492188101583602*a(n-19) +756635414359131*a(n-20) -15127411602979766*a(n-21) -4996517564711412*a(n-22) +124488915629652484*a(n-23) +32496342097994312*a(n-24) -830961220175609104*a(n-25) -217952927487180360*a(n-26) +4471006873093739800*a(n-27) +1356224545195754860*a(n-28) -19189501086495681880*a(n-29) -6829521421681422792*a(n-30) +64885315804531962064*a(n-31) +25455961312177735008*a(n-32) -171074565270467560384*a(n-33) -66023270051350386176*a(n-34) +350852776730555653120*a(n-35) +111115747477690885952*a(n-36) -562968030704836048256*a(n-37) -102780461262027908992*a(n-38) +705293155294335987968*a(n-39) -1905443632362091008*a(n-40) -673839571496082251776*a(n-41) +149968516817181865984*a(n-42) +463807639149162463232*a(n-43) -222954648389494145024*a(n-44) -202119207628642238464*a(n-45) +174410817888004440064*a(n-46) +32943327636122697728*a(n-47) -77835693049096830976*a(n-48) +15691242889927983104*a(n-49) +16793314088391802880*a(n-50) -9742537633650704384*a(n-51) -56226216776040448*a(n-52) +1727131956136640512*a(n-53) -597215426987950080*a(n-54) +331158386638848*a(n-55) +57745072535371776*a(n-56) -19695514744258560*a(n-57) +3305731101032448*a(n-58) -294085000691712*a(n-59) +11132555231232*a(n-60)

Example

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

Crossrefs

Sequence in context: A365874 A319617 A300162 * A069758 A116678 A218845

Adjacent sequences: A211256 A211257 A211258 * A211260 A211261 A211262

Keyword

nonn

Author

R. H. Hardin Apr 06 2012

Status

approved