cp's OEIS Frontend

A219032 Number of distinct squares as subwords of decimal representation of n-th square.

%I A219032 #12 Oct 20 2021 00:31:45
%S A219032 1,1,1,1,2,1,1,3,2,2,3,2,3,4,3,2,2,2,2,3,3,3,2,2,1,2,1,2,2,3,3,3,4,4,
%T A219032 2,4,3,4,4,2,4,4,4,5,4,3,3,3,3,4,3,3,3,3,4,3,3,5,4,4,3,2,2,2,4,4,2,3,
%U A219032 2,3,6,4,3,2,2,3,1,2,3,3,5,2,2,2,2,3
%N A219032 Number of distinct squares as subwords of decimal representation of n-th square.
%C A219032 a(n) is the number of squares in n-th row of triangle A219031.
%H A219032 Reinhard Zumkeller, <a href="/A219032/b219032.txt">Table of n, a(n) for n = 0..10000</a>
%F A219032 a(n) = Sum_{k=0..A120004(n^2)} A010052(A219031(n,k)).
%e A219032 .   n   row n in A219031
%e A219032 .  -----------------------------
%e A219032 .  20   [0, 4, 40, 400]            a(20) = #{0, 4, 400} = 3;
%e A219032 .  21   [1, 4, 41, 44, 441]        a(21) = #{1, 4, 441} = 3;
%e A219032 .  22   [4, 8, 48, 84, 484]        a(22) = #{4, 484} = 2;
%e A219032 .  23   [2, 5, 9, 29, 52, 529]     a(23) = #{9, 529} = 2;
%e A219032 .  24   [5, 6, 7, 57, 76, 576]     a(24) = #{576} = 1;
%e A219032 .  25   [2, 5, 6, 25, 62, 625]     a(25) = #{25, 625} = 2.
%o A219032 (Haskell)
%o A219032 a219032 = sum . map a010052 . a219031_row
%o A219032 (Python)
%o A219032 from sympy import integer_nthroot
%o A219032 def A219032(n):
%o A219032     s = str(n*n)
%o A219032     m = len(s)
%o A219032     return len(set(filter(lambda x: integer_nthroot(x,2)[1], (int(s[i:j]) for i in range(m) for j in range(i+1,m+1))))) # _Chai Wah Wu_, Oct 19 2021
%Y A219032 Cf. A010052, A120004, A219031.
%K A219032 nonn,base
%O A219032 0,5
%A A219032 _Reinhard Zumkeller_, Nov 10 2012