A216512 - OEIS

%I #19 Aug 06 2024 09:34:11

%S 1,0,0,1,0,0,1,1,1,0,1,0,0,0,0,2,0,0,0,0,0,0,1,0,1,0,0,1,1,0,0,2,0,0,

%T 0,1,1,0,0,0,0,0,1,1,0,0,0,0,1,0,0,0,1,0,0,1,0,0,0,0,0,0,1,3,0,0,1,0,

%U 0,0,1,1,0,0,0,0,1,0,1,0,1,0,0,0,0,0,0

%N Number of nonnegative integer solutions to the equation a^2 + 7*b^2 = n.

%H Aung Phone Maw, <a href="https://arxiv.org/abs/2408.01763">On the Number of Ways a Natural Number Can Be Written in the Form 7a^2+b^2</a>, arXiv:2408.01763 [math.GM], 2024.

%t r[n_] := Reduce[x >= 0 && y >= 0 && x^2 + 7 y^2 == n, Integers];

%t a[n_] := Which[rn = r[n]; rn === False, 0, Head[rn] === And, 1, Head[rn] === Or, Length[rn], True, -1];

%t Table[a[n], {n, 1, 87}] (* _Jean-François Alcover_, Jun 24 2017 *)

%Y Cf. A020670.

%K nonn

%O 1,16

%A _V. Raman_, Sep 08 2012