|
%I #12 Aug 08 2024 08:33:36
%S 11,121,31,388,961,105,4794,5450,11025,342,40416,188958,120738,116964,
%T 1044,375698,4182458,14855514,2326103,1089936,3159,4128762,101698908,
%U 1030363654,993542957,40102656,9979281,9735,41424210,2972878486,80122222262,208801521397,53115687500,663777212,94770225,28302
%N T(n,k) is the number of (n+2) X k 0..2 arrays with all rows having a nonnegative second derivative, and all 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.
%H R. H. Hardin, <a href="/A223391/b223391.txt">Table of n, a(n) for n = 1..47</a>
%e Table starts:
%e ....11.......121.........388..........4794..........40416.........375698
%e ....31.......961........5450........188958........4182458......101698908
%e ...105.....11025......120738......14855514.....1030363654....80122222262
%e ...342....116964.....2326103.....993542957...208801521397.49244499538437
%e ..1044...1089936....40102656...53115687500.31140652265964
%e ..3159...9979281...663777212.2791742360102
%e ..9735..94770225.11304765020
%e .28302.801003204
%e .87129
%e Some solutions for n=1 and k=4:
%e ..2..0..2..2....2..2..2..2....1..0..0..2....1..1..2..2....1..1..1..1
%e ..1..0..0..0....1..0..0..0....1..0..0..0....1..1..0..0....1..0..0..1
%e ..2..2..0..1....1..0..0..2....2..1..1..1....2..2..0..0....2..2..1..2
%K nonn,tabl,changed
%O 1,1
%A _R. H. Hardin_, Mar 19 2013
|
