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 A240127 #21 Oct 03 2024 11:06:30 %S A240127 1,1,1,1,2,2,1,3,3,3,5,5,6,10,9,10,17,20,18,31,34,38,52,62,65,98,108, %T A240127 113,160,190,204,271,322,352,448,533,572,757,863,956,1208,1401,1555, %U A240127 1931,2242,2499,3034,3527,3938,4772,5529,6108,7368,8524,9478,11301 %N A240127 Number of partitions of n such that the sum of squares of the parts is a square. %H A240127 Alois P. Heinz, <a href="/A240127/b240127.txt">Table of n, a(n) for n = 0..495</a> (terms n = 1..100 from Charles R Greathouse IV) %e A240127 a(12) counts these 6 partitions: [12], [5,2,2,1,1,1], [4,4,1,1,1,1], [4,3,3,1,1], [3,3,3,3], [2,2,1,1,1,1,1,1,1,1]. %t A240127 f[x_] := x^(1/2); z = 26; ColumnForm[t = Map[Select[IntegerPartitions[#], IntegerQ[f[Total[#^2]]] &] &, Range[z]] ](* shows the partitions *) %t A240127 t2 = Map[Length[Select[IntegerPartitions[#], IntegerQ[f[Total[#^2]]] &]] &, Range[40]] (* A240127 *) (* _Peter J. C. Moses_, Apr 01 2014 *) %o A240127 (PARI) a(n)=my(s); forpart(v=n, s+=issquare(sum(i=1,#v, v[i]^2))); s \\ _Charles R Greathouse IV_, Mar 06 2017 %Y A240127 Cf. A240128. %K A240127 nonn %O A240127 0,5 %A A240127 _Clark Kimberling_, Apr 02 2014 %E A240127 a(0)=1 prepended by _Alois P. Heinz_, Oct 03 2024