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A225437 Numbers of triples {x, y, z} such that z >= y > 0 and triangular(x) + triangular(y) * triangular(z) = 2^n. 2
1, 1, 2, 0, 4, 0, 5, 1, 7, 0, 4, 0, 18, 0, 2, 0, 17, 0, 16, 0, 15, 0, 9, 0, 39, 0, 9, 0, 61, 0, 10, 3, 27, 0, 18, 0, 56, 0, 8, 0, 80, 0, 48, 1, 41, 0, 12, 0, 118, 1, 10, 0, 90, 0, 30, 2, 24, 0, 24 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..58.

EXAMPLE

{0, 1, 1} is the only triple producing 2^0, so a(0) = 1.

{1, 1, 3} and {3, 1, 1} are the triples producing 2^2, so a(2) = 2.

PROG

(C)

#include <stdio.h>

#include <math.h>

typedef unsigned long long U64;

U64 isTriangular(U64 a) {  // ! Must be a <= (1<<63)

    U64 s = sqrt(a*2);

    if (a>=(1ULL<<63)) {

      if (a==(1ULL<<63)) return 0;

      printf("Error: a = %llu\n", a), exit(1);

    }

    return (s*(s+1)/2 == a);

}

int main() {

  U64 c, n, x, tx, y, ty, z, prod;

  for (n = 1; n>0 && n <= (1ULL<<63); n+=n) {

    for (c = 0, x = tx = 0; tx <= n; ++x, tx+=x)

      for (z=prod=n-tx, y=ty=1; ty<=z; ++y, ty+=y, z=prod/ty)

        if ((z * ty == prod) && isTriangular(z))  c++;

    printf("%llu, ", c);

  }

  return 0;

}

CROSSREFS

Cf. A000217, A224928, A225536.

Sequence in context: A286663 A114402 A035647 * A065806 A331185 A228087

Adjacent sequences:  A225434 A225435 A225436 * A225438 A225439 A225440

KEYWORD

nonn,hard,more

AUTHOR

Alex Ratushnyak, May 08 2013

STATUS

approved

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Last modified June 4 11:32 EDT 2020. Contains 334825 sequences. (Running on oeis4.)