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%I #11 Mar 04 2020 20:19:21
%S 0,1,0,1,2,0,2,1,1,0,2,3,1,2,0,3,2,2,1,1,0,1,2,2,3,3,4,0,2,1,3,2,4,3,
%T 1,0,2,3,1,2,2,3,1,2,0,3,2,2,1,3,2,2,1,1,0,3,4,2,3,1,2,2,3,1,2,0,4,3,
%U 3,2,2,1,3,2,2,1,1,0,2,3,3,4,4,5,1,2,2,3,3,4,0,3,2,4,3,5,4,2,1,3,2,4,3,1,0,3,4,2,3,3,4,2,3,1,2,2,3,1,2,0
%N Lower triangular region of A231713; A triangular table read by rows: T(n,k) = sum of absolute values of digit differences in the factorial base representations (A007623) of n and k, where (n, k) = (0,0), (1,0), (1,1), (2,0), (2,1), (2,2), ..., n >= 0 and (0 <= k <= n).
%H Antti Karttunen, <a href="/A231714/b231714.txt">Rows n = 0..120 of triangle, flattened</a>
%F a(n) = A231713(A003056(n),A002262(n)). [As a sequence, this is obtained by taking a subsection from array A231713.]
%F T(n,0) = A034968(n). [The leftmost column]
%F Each entry T(n,k) >= A230417(n,k).
%e This triangular table begins as:
%e 0;
%e 1, 0;
%e 1, 2, 0;
%e 2, 1, 1, 0;
%e 2, 3, 1, 2, 0;
%e 3, 2, 2, 1, 1, 0;
%e 1, 2, 2, 3, 3, 4, 0;
%e 2, 1, 3, 2, 4, 3, 1, 0;
%e ...
%e Please see A231713 for examples how the terms are computed.
%o (Scheme)
%o (define (A231714 n) (A231713bi (A003056 n) (A002262 n)))
%o (define (A231713bi x y) (let loop ((x x) (y y) (i 2) (d 0)) (cond ((and (zero? x) (zero? y)) d) (else (loop (floor->exact (/ x i)) (floor->exact (/ y i)) (+ i 1) (+ d (abs (- (modulo x i) (modulo y i)))))))))
%Y The leftmost column: A034968.
%Y This is a lower, or equivalently, an upper triangular subregion of symmetric square array A231713. Cf. A230417.
%K nonn,base,tabl
%O 0,5
%A _Antti Karttunen_, Nov 12 2013
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