A219032 - OEIS

%I #12 Oct 20 2021 00:31:45

%S 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 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 2,3,6,4,3,2,2,3,1,2,3,3,5,2,2,2,2,3

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

%C a(n) is the number of squares in n-th row of triangle A219031.

%H Reinhard Zumkeller, <a href="/A219032/b219032.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = Sum_{k=0..A120004(n^2)} A010052(A219031(n,k)).

%e .   n   row n in A219031

%e .  -----------------------------

%e .  20   [0, 4, 40, 400]            a(20) = #{0, 4, 400} = 3;

%e .  21   [1, 4, 41, 44, 441]        a(21) = #{1, 4, 441} = 3;

%e .  22   [4, 8, 48, 84, 484]        a(22) = #{4, 484} = 2;

%e .  23   [2, 5, 9, 29, 52, 529]     a(23) = #{9, 529} = 2;

%e .  24   [5, 6, 7, 57, 76, 576]     a(24) = #{576} = 1;

%e .  25   [2, 5, 6, 25, 62, 625]     a(25) = #{25, 625} = 2.

%o (Haskell)

%o a219032 = sum . map a010052 . a219031_row

%o (Python)

%o from sympy import integer_nthroot

%o def A219032(n):

%o     s = str(n*n)

%o     m = len(s)

%o     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 Cf. A010052, A120004, A219031.

%K nonn,base

%O 0,5

%A _Reinhard Zumkeller_, Nov 10 2012