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A230420 Triangle T(n,k) giving the number of terms of A219666 which have n digits (A084558) in their factorial base expansion and whose most significant digit (A099563) in that base is k.

%I A230420 #10 Oct 19 2013 11:00:01
%S A230420 1,1,1,2,2,1,6,5,4,4,22,19,16,14,12,94,82,73,65,59,55,479,432,395,362,
%T A230420 336,314,293,2886,2667,2482,2324,2189,2073,1971,1881,20276,19123,
%U A230420 18124,17249,16473,15775,15140,14555,14011,164224,156961,150389,144378,138828,133664,128831,124289,120010,115974
%N A230420 Triangle T(n,k) giving the number of terms of A219666 which have n digits (A084558) in their factorial base expansion and whose most significant digit (A099563) in that base is k.
%C A230420 See A007623 for the factorial number system representation.
%F A230420 T(n,k) = 1 + A219652(A230429(n,k)) - A219652(A230428(n,k)).
%e A230420 The first rows of this triangular table are:
%e A230420 1;
%e A230420 1, 1;
%e A230420 2, 2, 1;
%e A230420 6, 5, 4, 4;
%e A230420 22, 19, 16, 14, 12;
%e A230420 94, 82, 73, 65, 59, 55;
%e A230420 ...
%e A230420 T(4,2) = 5 as only the terms 48, 52, 57, 63 and 70 of A219666 (with factorial base representations 2000, 2020, 2111, 2211 and 2320) have four significant digits in the factorial base, with the most significant digit being 2.
%o A230420 (Scheme)
%o A230420 (define (A230420 n) (if (<= n 3) 1 (let loop ((i (A230429 n)) (s 0)) (cond ((not (= (A099563 i) (A002260 n))) s) (else (loop (A219651 i) (+ 1 s)))))))
%Y A230420 Transpose: A230421. Row sums: A219661. Cf. also A230428, A230429, A219652, A219666.
%K A230420 nonn,base,tabl
%O A230420 1,4
%A A230420 _Antti Karttunen_, Oct 18 2013