A219032 - OEIS

A219032

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

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, 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, 2, 3, 6, 4, 3, 2, 2, 3, 1, 2, 3, 3, 5, 2, 2, 2, 2, 3

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OFFSET

0,5

COMMENTS

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

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

FORMULA

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

EXAMPLE

. n row n in A219031

. -----------------------------

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

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

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

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

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

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

PROG

(Haskell)

a219032 = sum . map a010052 . a219031_row

(Python)

from sympy import integer_nthroot

def A219032(n):

s = str(n*n)

m = len(s)

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

CROSSREFS

Cf. A010052, A120004, A219031.

Sequence in context: A390353 A060118 A329143 * A234567 A241950 A316776

Adjacent sequences: A219029 A219030 A219031 * A219033 A219034 A219035

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Nov 10 2012

STATUS

approved