%I #5 Mar 31 2012 12:36:16
%S 4,14,14,28,44,28,46,94,94,46,68,158,200,158,68,94,238,342,342,238,94,
%T 124,330,524,596,524,330,124,158,434,732,926,926,732,434,158,196,550,
%U 972,1308,1444,1308,972,550,196,238,678,1236,1754,2060,2060,1754,1236,678
%N T(n,k)=Number of right triangles on a (n+1)X(k+1) grid
%C Table starts
%C ...4..14...28...46...68...94...124...158...196...238...284...334...388...446
%C ..14..44...94..158..238..330...434...550...678...818...970..1134..1310..1498
%C ..28..94..200..342..524..732...972..1236..1524..1840..2180..2544..2932..3344
%C ..46.158..342..596..926.1308..1754..2250..2794..3390..4026..4702..5426..6190
%C ..68.238..524..926.1444.2060..2784..3596..4492..5470..6516..7630..8820.10070
%C ..94.330..732.1308.2060.2960..4032..5250..6604..8082..9684.11388.13220.15144
%C .124.434..972.1754.2784.4032..5520..7224..9128.11218.13500.15938.18568.21328
%C .158.550.1236.2250.3596.5250..7224..9496.12044.14860.17948.21266.24852.28634
%C .196.678.1524.2794.4492.6604..9128.12044.15332.18990.23012.27354.32052.37032
%C .238.818.1840.3390.5470.8082.11218.14860.18990.23596.28678.34190.40166.46522
%H R. H. Hardin, <a href="/A189814/b189814.txt">Table of n, a(n) for n = 1..10025</a>
%F Empirical for columns
%F k=1: a(n) = 2*n^2 + 4*n - 2
%F k=2: a(n) = 6*n^2 + 26*n - 42 for n>3
%F k=3: a(n) = 12*n^2 + 88*n - 240 for n>8
%F k=4: a(n) = 20*n^2 + 228*n - 930 for n>15
%F k=5: a(n) = 30*n^2 + 468*n - 2478 for n>24
%F k=6: a(n) = 42*n^2 + 886*n - 6080 for n>35
%F k=7: a(n) = 56*n^2 + 1480*n - 12216 for n>48
%F k=8: a(n) = 72*n^2 + 2344*n - 23112 for n>63
%F k=9: a(n) = 90*n^2 + 3516*n - 40434 for n>80
%F k=10: a(n) = 110*n^2 + 5090*n - 67626 for n>99
%F k=11: a(n) = 132*n^2 + 7016*n - 105016 for n>120
%F k=12: a(n) = 156*n^2 + 9564*n - 162094 for n>143
%F k=13: a(n) = 182*n^2 + 12572*n - 236518 for n>168
%F k=14: a(n) = 210*n^2 + 16230*n - 337676 for n>195
%e Some solutions for n=3 k=3
%e ..2..3....2..1....0..2....0..1....3..1....1..3....4..2....2..2....1..1....3..2
%e ..1..2....0..3....0..3....0..2....1..3....1..2....2..1....2..1....0..2....1..3
%e ..4..1....3..2....4..2....5..1....5..3....4..3....5..0....5..2....2..2....2..0
%Y Column 1 is -A147973(n+4)
%Y Diagonal is A077435(n+1)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Apr 28 2011