A121705 Triangle read by rows: 5^n expressed as the sum of two squares.

0, 1, 1, 2, 0, 5, 3, 4, 2, 11, 5, 10, 0, 25, 7, 24, 15, 20, 10, 55, 25, 50, 38, 41, 0, 125, 35, 120, 44, 117, 75, 100, 29, 278, 50, 275, 125, 250, 190, 205, 0, 625, 175, 600, 220, 585, 336, 527, 375, 500, 145, 1390, 250, 1375, 625, 1250, 718, 1199, 950, 1025, 0, 3125

Offset: 0

Author

Zak Seidov, Sep 10 2006

Keywords

• nonn
• tabf

Examples

			5^n expressed as the sum of two squares: 5^n = x^2 + y^2, 0 <= x < y.
Number of solutions for n=0,1,...: a(n)=1,1,2,2,3,3,4,4,5,5,6,6,...
Triangle of solutions for n=0,1,...:
  {x,y}
  {{0,1}},
  {{1,2}},
  {{0,5},{3,4}},
  {{2,11},{5,10}},
  {{0,25},{7,24},{15,20}},
  {{10,55},{25,50},{38,41}},
  {{0,125},{35,120},{44,117},{75,100}},
  {{29,278},{50,275},{125,250},{190,205}},
  {{0,625},{175,600},{220,585},{336,527},{375,500}},
  {{145,1390},{250,1375},{625,1250},{718,1199},{950,1025}},
  {{0,3125},{237,3116},{875,3000},{1100,2925},{1680,2635},{1875,2500}},
  {{725,6950},{1250,6875},{2642,6469},{3125,6250},{3590,5995},{4750,5125}},
  {{0,15625},{1185,15580},{4375,15000},{5500,14625},{8400,13175},{9375,12500},{10296,11753}}
		

Crossrefs

Cf. A004431, A006496, A024507, A120905.