a(1)=3 because 3^2=1+2*4 and 1,2,4 are in geometric sequence
a(2)=102 because 102^2=36+72*144 and 36,72,144 are in geometric sequence
a(3)=130 because 130^2=25+75*225 and 25,75,225 are in geometric sequence
a(4)=312 because 312^2=8+92*1058 and ...
a(5)=759 because 759^2=81+360*1600
a(6)=2496 because 2496^2=512+1472*4232
a(7)=2706 because 2706^2=1936+2420*3025
a(8)=3465 because 3465^2=1225+2450*4900
a(9)=6072 because 6072^2=5184+5760*6400
a(10)=6111 because 6111^2=3969+5292*7056
a(11)=8424 because 8424^2=5832+7452*9522
a(12)=14004 because 14004^2=432+4392*44652
a(13)=16005 because 16005^2=1089+6534*39204
a(14)=36897 because 36897^2=21609+30870*44100
a(15)=37156 because 37156^2=12544+25872*53361
a(16)=92385 because 92385^2=50625+75600*112896
a(17)=98640 because 98640^2=50625+78975*123201
a(18)=112032 because 112032^2=27648+70272*178608
a(19)=117708 because 117708^2=41616+83232*166464
a(20)=128040 because 128040^2=69696+104544*156816
a(21)=351260 because 351260^2=67600+202800*608400
a(22)=378108 because 378108^2=314928+355752*401868
a(23)=740050 because 740050^2=521284+658464*831744
No other numbers smaller than a million have squares that can be expressed this way.
Contribution from Donovan Johnson, Jul 30 2010: (Start)
a(24)=1346400 because 1346400^2=135000+625500*2898150
a(25)=1371900 because 1371900^2=10000+266000*7075600
a(26)=1898130 because 1898130^2=6084+279864*12873744
a(27)=3998607 because 3998607^2=1413721+2827442*5654884
a(28)=5986575 because 5986575^2=1157625+3461850*10352580
a(29)=6082065 because 6082065^2=4348377+5438466*6801828
a(30)=6631596 because 6631596^2=1944+440532*99829446
a(31)=6741214 because 6741214^2=334084+2476152*18352656
a(32)=7692804 because 7692804^2=444528+2974104*19898172
(End)
