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A260305 We represent square arrays of single-digit entries by the single number formed by reading them row-by-row, top-to-bottom. Sequence gives list of k X k square grids formed from single-digit numbers having property that reading across each row and each column gives a square number.

%I A260305 #47 Jan 12 2017 20:22:57
%S A260305 1,4,9,1664,3664,6449,8116,121256169,121289196,144400400,144484441,
%T A260305 169676961,361676169,441400100,441484144,529256961,729256961,
%U A260305 841400100,841484144,961676169,1296202592166561,1369384464009409
%N A260305 We represent square arrays of single-digit entries by the single number formed by reading them row-by-row, top-to-bottom. Sequence gives list of k X k square grids formed from single-digit numbers having property that reading across each row and each column gives a square number.
%C A260305 Suppose for example a term has 9 digits, say abcdefghi. This means that the grid is
%C A260305 abc
%C A260305 def
%C A260305 ghi
%C A260305 and that the decimal concatenations abc, def, ghi, adg, beh, cfi are all squares. E.g., for 121256169 we see that 121, 256, 169, 121, 256 and 169 are squares.
%C A260305 There are 3 grids of size 1 X 1.
%C A260305 There are 4 grids of size 2 X 2.
%C A260305 There are 13 grids of size 3 X 3.
%C A260305 There are 14 grids of size 4 X 4.
%C A260305 There are 76 grids of size 5 X 5.
%C A260305 There are 108 grids of size 6 X 6.
%C A260305 There are 459 grids of size 7 X 7.
%C A260305 There are 844 grids of size 8 X 8.
%C A260305 No leading zeros are allowed in the rows and columns.
%H A260305 Luca Petrone, <a href="/A260305/b260305.txt">Table of n, a(n) for n = 1..1521</a>
%e A260305 169676961 is in the sequence, so the 3 X 3 grid is:
%e A260305 (1 6 9)
%e A260305 (6 7 6)
%e A260305 (9 6 1)
%e A260305 146414494469696449441461 is in the sequence; this is a 25-digit term, and the 5 X 5 grid is:
%e A260305 (1 4 6 4 1)
%e A260305 (4 4 9 4 4)
%e A260305 (6 9 6 9 6)
%e A260305 (4 4 9 4 4)
%e A260305 (1 4 6 4 1)
%Y A260305 Cf. A105074.
%K A260305 nonn,base
%O A260305 1,2
%A A260305 _Pieter Post_, Nov 10 2015
%E A260305 Corrected and extended by _Luca Petrone_, Jan 08 2017