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 A223495 T(n,k)=Number of (n+2)Xk 0..3 arrays with all rows having a nonnegative second derivative, and all and columns having a positive second derivative in a quadratic least squares fit, with one and two element arrays taken as having a zero second derivative 6

%I #4 Mar 20 2013 16:01:07

%S 28,784,106,5264,11236,466,164650,172262,217156,1970,3726450,20316988,

%T 7974566,3880900,7904,89957891,1634694162,4307975642,332428881,

%U 62473216,31897,2474370640,141426507841,1422650942236,802504089833,12184078320

%N T(n,k)=Number of (n+2)Xk 0..3 arrays with all rows having a nonnegative second derivative, and all and columns having a positive second derivative in a quadratic least squares fit, with one and two element arrays taken as having a zero second derivative

%C Table starts

%C .....28.........784.........5264..........164650..........3726450

%C ....106.......11236.......172262........20316988.......1634694162

%C ....466......217156......7974566......4307975642....1422650942236

%C ...1970.....3880900....332428881....802504089833.1045485381621951

%C ...7904....62473216..12184078320.122450764432500

%C ..31897..1017418609.451243568715

%C .130224.16958290176

%C .508551

%H R. H. Hardin, <a href="/A223495/b223495.txt">Table of n, a(n) for n = 1..39</a>

%e Some solutions for n=1 k=4

%e ..3..3..3..3....2..0..2..2....2..1..1..0....0..0..2..2....0..2..1..3

%e ..2..0..2..1....0..0..0..0....0..0..0..0....0..0..0..1....1..1..0..2

%e ..3..0..3..0....2..1..0..1....1..3..0..3....1..1..0..3....3..3..2..2

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Mar 20 2013

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Last modified April 16 05:35 EDT 2024. Contains 371697 sequences. (Running on oeis4.)