A378149 a(n) is the number of distinct integer-sided right trapezoids with exactly one pair of parallel sides and area n.

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 2, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 3, 0, 1, 1, 1, 1, 2, 0, 1, 1, 2, 0, 4, 0, 0, 2, 1, 0, 3, 0, 2, 1, 0, 0, 4, 1, 1, 1, 1, 0, 3, 0, 1, 2, 1, 1, 5, 0, 1, 1, 2, 0, 4, 0, 1, 3, 1, 0, 5, 0, 2, 2, 1, 0, 3, 1, 1, 1

Offset

1,18

Links

Felix Huber, Table of n, a(n) for n = 1..10000

Felix Huber, Integer-sided right trapezoids with area n

Eric Weisstein's World of Mathematics, Right Trapezoid

Formula

a(p) = 0 for prime p.

Example

a(54) = 4 because there are 4 distinct integer-sided right trapezoids [p, r, q, d, h] (p and q are parallel, r is rectangular to p and q, height h = r) with area 54: [13, 6, 5, 10, 6], [20, 3, 16, 5, 3], [7, 12, 2, 13, 12], [15, 4, 12, 5, 4].

Maple

A378149:=proc(n)
   local a, m, q, M;
   a:=0;
   M:=map(x->x/2, NumberTheory:-Divisors(2*n) minus {1, 2});
   for m in M do
      for q from 1 to m-3/2 do
         if issqr((2*(m-q))^2+(n/m)^2) then
            a:=a+1
         fi
      od
   od;
   return a
end proc;
seq(A378149(n), n=1..87);

Crossrefs

Cf. A027750, A214602, A340858, A340859, A340860, A374594, A378148, A378150.

Sequence in context: A337976 A378150 A125005 * A309367 A347709 A122179

Adjacent sequences: A378146 A378147 A378148 * A378150 A378151 A378152

Keyword

nonn

Author

Felix Huber, Dec 04 2024

Status

approved