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.
%I A376005 #5 Sep 27 2024 00:03:24 %S A376005 0,0,2,2,4,6,10,8,14,16,18,22,26,22,38,36,36,44,48,42,60,62,62,64,78, %T A376005 68,88,90,78,102,114,92,120,104,118,134,144,122,148,156,138,168,178, %U A376005 142,194,194,186,192,200,188,232,230,212,218,252,224,274,272,236 %N A376005 For integers >=2, the number of integer solutions to sqrt((n^2-c)*b^2 + c*(b+1)^2) where b and c are positive integers and c < n^2. %C A376005 a(n) = count(k) of A375336(n, k) for each n >= 2. %C A376005 Omitting n < 2, which yield no c values that meet the rubric. %e A376005 A375336 rows n = 2 and n = 3 are empty, so a(2) = 0 and a(3) = 0. %e A376005 A375336 rows n = 4 and n = 5 each contain 2 terms, so a(4) = 2 and a(5) = 2. %o A376005 (PARI) a(n)=my(d=n^2, t=n, an=0); while(t<=n^3/8, my(b=floor(sqrt(t^2/d)), r=t^2-d*b^2); if (r && r%(b*2+1)==0, an++); t++); an %o A376005 for(n=2, 100, print(n, " ", a(n))) %Y A376005 Cf. A375336. %K A376005 nonn %O A376005 2,3 %A A376005 _Charles L. Hohn_, Sep 05 2024