A260305 - OEIS

%I #47 Jan 12 2017 20:22:57

%S 1,4,9,1664,3664,6449,8116,121256169,121289196,144400400,144484441,

%T 169676961,361676169,441400100,441484144,529256961,729256961,

%U 841400100,841484144,961676169,1296202592166561,1369384464009409

%N 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 Suppose for example a term has 9 digits, say abcdefghi. This means that the grid is

%C abc

%C def

%C ghi

%C 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 There are 3 grids of size 1 X 1.

%C There are 4 grids of size 2 X 2.

%C There are 13 grids of size 3 X 3.

%C There are 14 grids of size 4 X 4.

%C There are 76 grids of size 5 X 5.

%C There are 108 grids of size 6 X 6.

%C There are 459 grids of size 7 X 7.

%C There are 844 grids of size 8 X 8.

%C No leading zeros are allowed in the rows and columns.

%H Luca Petrone, <a href="/A260305/b260305.txt">Table of n, a(n) for n = 1..1521</a>

%e 169676961 is in the sequence, so the 3 X 3 grid is:

%e (1 6 9)

%e (6 7 6)

%e (9 6 1)

%e 146414494469696449441461 is in the sequence; this is a 25-digit term, and the 5 X 5 grid is:

%e (1 4 6 4 1)

%e (4 4 9 4 4)

%e (6 9 6 9 6)

%e (4 4 9 4 4)

%e (1 4 6 4 1)

%Y Cf. A105074.

%K nonn,base

%O 1,2

%A _Pieter Post_, Nov 10 2015

%E Corrected and extended by _Luca Petrone_, Jan 08 2017