cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A374091 a(n) is the smallest nonnegative integer k where exactly n ordered pairs of positive integers (x, y) exist such that x^2 + 3*x*y + y^2 = k.

Original entry on oeis.org

0, 5, 11, 605, 209, 73205, 2299, 8857805, 6061, 218405, 278179
Offset: 0

Views

Author

Seiichi Manyama, Jun 28 2024

Keywords

Comments

a(n) is the smallest nonnegative k such that A374089(k) = n.
a(n) is of the form 5*k^2 if and only if n is odd.
a(12) = 66671.
a(14) = 5285401.
a(15) = 26427005.
a(16) = 187891.
a(18) = 1266749.
a(20) = 8067191.
a(21) = 3197667605. - Chai Wah Wu, Jun 29 2024
a(24) = 2066801.
a(26) = 36735721.
a(27) = 183678605. - Chai Wah Wu, Jun 28 2024

Crossrefs

Cf. A328151, A374090.
Cf. A374089, A374095.

Formula

a(2*n) = A374095(n).
a(n) <= 5*11^(n-1) for all n >= 1. - Jason Yuen, Jun 29 2024

A374088 Number of ordered pairs (x,y) of positive integers such that x^2 + x*y + y^2 = n.

Original entry on oeis.org

0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 1, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, 2
Offset: 0

Views

Author

Seiichi Manyama, Jun 28 2024

Keywords

Links

Crossrefs

Cf. A063725, A374089.

Programs

  • Python
    from sympy.abc import x, y
from sympy.solvers.diophantine.diophantine import diop_quadratic
def A374088(n): return sum(1 for d in diop_quadratic(x*(x+y)+y**2-n) if d[0]>0 and d[1]>0) # Chai Wah Wu, Jun 28 2024
Showing 1-2 of 2 results.

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