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A237448 Square array T(row >= 1, col >= 1): The first row, row=1, T(1,col) = col = A000027. When row > col, T(row,col) = row, otherwise (when 1 < row <= col), T(row,col) = row-1.

%I A237448 #17 Oct 28 2019 02:41:21
%S A237448 1,2,2,3,1,3,4,1,3,4,5,1,2,4,5,6,1,2,4,5,6,7,1,2,3,5,6,7,8,1,2,3,5,6,
%T A237448 7,8,9,1,2,3,4,6,7,8,9,10,1,2,3,4,6,7,8,9,10,11,1,2,3,4,5,7,8,9,10,11,
%U A237448 12,1,2,3,4,5,7,8,9,10,11,12,13,1,2,3,4,5,6,8,9,10,11,12,13
%N A237448 Square array T(row >= 1, col >= 1): The first row, row=1, T(1,col) = col = A000027. When row > col, T(row,col) = row, otherwise (when 1 < row <= col), T(row,col) = row-1.
%C A237448 This is transpose of A237447, please see comments there.
%H A237448 Antti Karttunen, <a href="/A237448/b237448.txt">Table of first 144 antidiagonals of array, flattened</a>
%F A237448 As a one-dimensional sequence:
%F A237448 If A010054(n-1) = 1 [that is, if n is in A000124], then a(n) = A002024(n), otherwise, if A004736(n) < A002260(n), a(n) = A002260(n), and if A004736(n) >= A002260(n), a(n) = A002260(n)-1.
%F A237448 Equivalently, as a square array T:
%F A237448 When col < row, T(row,col) = row, for 1 < row <= col, T(row,col) = row-1, and for the first row T(1,col) = col = A000027(col).
%F A237448 Can be computed also as a transposed version of the infinite limit of the finite square arrays in sequence A237265: T(row,col) = A237265((A000330(max(row,col)-1)+1) + (max(row,col)*(col-1)) + (row-1)).
%e A237448 The top left 9 X 9 corner of this infinite square array:
%e A237448   1 2 3 4 5 6 7 8 9
%e A237448   2 1 1 1 1 1 1 1 1
%e A237448   3 3 2 2 2 2 2 2 2
%e A237448   4 4 4 3 3 3 3 3 3
%e A237448   5 5 5 5 4 4 4 4 4
%e A237448   6 6 6 6 6 5 5 5 5
%e A237448   7 7 7 7 7 7 6 6 6
%e A237448   8 8 8 8 8 8 8 7 7
%e A237448   9 9 9 9 9 9 9 9 8
%o A237448 (Scheme)
%o A237448 (define (A237448 n) (cond ((= 1 (A010054 (- n 1))) (A002024 n)) ((< (A004736 n) (A002260 n)) (A002260 n)) (else (- (A002260 n) 1))))
%Y A237448 Transpose: A237447.
%Y A237448 The leftmost column and the topmost row: A000027. Second row: A054977. Central diagonal: A028310 (note the different starting offsets).
%Y A237448 Antidiagonal sums: A074148.
%Y A237448 Cf. A237265, A000330, A002024, A002260, A004736, A000124, A010054.
%K A237448 nonn,tabl,easy
%O A237448 1,2
%A A237448 _Antti Karttunen_, Feb 10 2014