login
Number of positive integer solutions to the equation a^2 + 10*b^2 = n.
2

%I #12 Jan 10 2015 03:10:18

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

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

%U 0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2

%N Number of positive integer solutions to the equation a^2 + 10*b^2 = n.

%H Charles R Greathouse IV, <a href="/A216579/b216579.txt">Table of n, a(n) for n = 1..10000</a>

%t a[ n_] := If[ n < 1, 0, Length@Select[ Range@Sqrt[ n/10], IntegerQ@Sqrt[ n - 10 #] &]]; (* _Michael Somos_, Jan 10 2015 *)

%o (PARI) a(n)=sum(b=1,sqrtint((n-1)\10),issquare(n-10*b^2)) \\ _Charles R Greathouse IV_, Nov 19 2014

%Y Cf. A020673, A033201.

%K nonn

%O 1,91

%A _V. Raman_, Sep 08 2012