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A081493 Triangle T(n,k) read by rows in which the n-th row begins with T(n,1) = n and contains n terms of an arithmetic progression with a common difference of (n-1).

%I A081493 #20 Mar 31 2025 14:34:56
%S A081493 1,2,3,3,5,7,4,7,10,13,5,9,13,17,21,6,11,16,21,26,31,7,13,19,25,31,37,
%T A081493 43,8,15,22,29,36,43,50,57,9,17,25,33,41,49,57,65,73,10,19,28,37,46,
%U A081493 55,64,73,82,91,11,21,31,41,51,61,71,81,91,101,111,12,23,34,45,56,67,78,89,100,111,122,133
%N A081493 Triangle T(n,k) read by rows in which the n-th row begins with T(n,1) = n and contains n terms of an arithmetic progression with a common difference of (n-1).
%C A081493 n-th row sum gives the sum corresponding to the magic square of order n.
%H A081493 Harvey P. Dale, <a href="/A081493/b081493.txt">Table of n, a(n) for n = 1..1000</a>
%F A081493 T(i,j) = i + (i-1)*(j-1). - _David Wasserman_, Jun 03 2004
%e A081493 Triangle T(n,k) begins:
%e A081493   1;
%e A081493   2,  3;
%e A081493   3,  5,  7;
%e A081493   4,  7, 10, 13;
%e A081493   5,  9, 13, 17, 21;
%e A081493   6, 11, 16, 21, 26, 31;
%e A081493   ...
%t A081493 Table[NestList[#+n-1&,n,n-1],{n,20}]//Flatten (* _Harvey P. Dale_, May 14 2023 *)
%Y A081493 Row sums are A006003.
%Y A081493 Central terms of rows give A001844.
%K A081493 nonn,tabl,easy
%O A081493 1,2
%A A081493 _Amarnath Murthy_, Mar 25 2003
%E A081493 Corrected and extended by _David Wasserman_, Jun 03 2004