[seqfan] Re: A contest for AMS/MAA meeting in January 2013

[юрий герасимов]

This sequence for "CONTEST": 

Goldbach's problem extended to primitive Pythagorean triangle: number of decompositions of n into unordered the half difference of total length of the legs and legth of the hypotenuse.

a(1) = 1 because (3 + 4 - 5)/2 = 1; 
a(2) = 1 because (5 +12 -13)/2 = 2; 
a(3) = 2 because (15 + 8 - 17)/2 = 3 and ((7 + 24 - 25)/2 = 3; 
a(4) = 1 because (9 + 40 - 41)/2 = 4; 
a(5) = 2 because (35 + 12 - 37)/2 = 5 and (11 + 60 - 61)/2 = 5; 
a(6) = 2 because (21 + 20 - 29)/2 = 6 and (13 + 84 - 85)/2 = 6; 
a(7) = 2 because (63 + 16 - 65)/2 = 7 and (15 + 112 - 113)/2 = 7; 
a(8) = 1 because (17 + 144 -145)/2 = 8; 
a(9) = 2 because (99 + 20 - 101)/2 = 9 and (19 + 180 - 181)/2 = 9; 
a(10) = 2 because (45 + 28 - 53)/2 = 10 and (21 + 220 - 221)/2 = 10; 
a(11) = 2 because (143 + 24 - 145)/2 = 11 and (23 + 264 - 265)/2 = 11; 
a(12) = 2 because (33 + 56 - 65)/2 = 12 and (....

Cf. A171611. 

Juri-Stepan Gerasimov, Dec 22 12 2012.