cp's OEIS Frontend

A075406 a(n) is the number of terms in the sum in A075405 (or 0 if no such square exists).

%I A075406 #15 Apr 16 2025 05:42:14
%S A075406 24,0,2,0,0,0,23,0,24,0,22898,0,96,0,97,0,23,11,0,2,96,59,0,0,24,0,33,
%T A075406 50,0,169,0,578,0,0,0,0,0,11,0,0,0,0,0,24,0,0,0,0,0,122,0,96,0,0,3479,
%U A075406 0,0,2075,0,33,0,0,0,242,218,0,50,0,0,0,0,0,122,36481,0,24,0,0,0,0,0,0,194,0,0,0,50,0,0,0,242,0,0,0,0,0,0,0,0,0
%N A075406 a(n) is the number of terms in the sum in A075405 (or 0 if no such square exists).
%C A075406 Note that a(n) is either 0 or a number in A001032.
%D A075406 See A180422.
%e A075406 a(1) = 25 because the sum 1^2+...+24^2 consists of 25 terms, see A075404.
%t A075406 s[n_, k_]:=Module[{m=n+k-1}, (m(m+1)(2m+1)-n(n-1)(2n-1))/6]; mx=40000; Table[k=2; While[k<mx && !IntegerQ[Sqrt[s[n, k]]], k++]; If[k==mx, 0, k], {n, 100}]
%Y A075406 Cf. A000330, A075404, A075405.
%K A075406 nonn
%O A075406 1,1
%A A075406 _Zak Seidov_, Sep 13 2002
%E A075406 Corrected and extended by _Lior Manor_, Sep 19 2002
%E A075406 Corrected and edited by _T. D. Noe_, Jan 21 2011