A123237 A000316-like neo-Hankel matrix determinant sequence.

1, -1, -12, 144, 2400, -28224, -1296000, 50808384, 2434614000, -85975622656, -8396400230400, 691198592910336, 65694715632000000, -4784543769600000000, -796566295447796966400, 112616674749446400000000, 17805426854398997299200000, -2223594618178251399873232896

Offset: 1

Author

Roger L. Bagula, Oct 06 2006

Keywords

• uned
• sign

Comments

This neo-Hankel matrix type is symmetrical about the diagonal: The average (i*(j+1)/2+j*(i+1)/2)/4 =(i+j+2*i*j)/4 term is based on the sum of integers n(n+1)/2. I get Log plot fit of an exponent: Det[M[n]]=c*n^4.2586 a0 = Table[Det[Table[ If[i + j - 1 > m, 0, Floor[(i + j + 2*i*j)/4]], {i, 1, m}, {j, 1, m}]], {m, 3, 20}]; a = N[Log[Abs[%]]]; g1 = ListPlot[a, PlotJoined -> True]; y[x_] = Fit[a, {1, x}, x] g2 = Plot[y[x], {x, 0, 20}]; Show[{g1, g2}]

Crossrefs

Cf. A000316.

Programs

Mathematica

Table[Det[Table[If[i + j - 1 > m, 0, Floor[(i + j + 2*i*j)/4]], {i, 1, m}, {j, 1, m}]], {m, 1, 20}]

Formula

mij=If[i + j - 1 > m, 0, Floor[(i + j + 2*i*j)/4]]