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

0,4

Links

Table of n, a(n) for n=0..61.

Example

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.

Sequence in context: A184854 A021491 A324654 * A071782 A328495 A297024

Adjacent sequences: A121702 A121703 A121704 * A121706 A121707 A121708

Keyword

nonn,tabf

Author

Zak Seidov, Sep 10 2006

Status

approved