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.

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, 336, 314, 293, 2886, 2667, 2482, 2324, 2189, 2073, 1971, 1881, 20276, 19123, 18124, 17249, 16473, 15775, 15140, 14555, 14011, 164224, 156961, 150389, 144378, 138828, 133664, 128831, 124289, 120010, 115974

Offset: 1

Author

Antti Karttunen, Oct 18 2013

Keywords

• nonn
• base
• tabl

Comments

See A007623 for the factorial number system representation.

Examples

			The first rows of this triangular table are:
1;
1, 1;
2, 2, 1;
6, 5, 4, 4;
22, 19, 16, 14, 12;
94, 82, 73, 65, 59, 55;
...
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.
		

Crossrefs

Transpose: A230421. Row sums: A219661. Cf. also A230428, A230429, A219652, A219666.

Programs

Scheme

(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)))))))

Formula

T(n,k) = 1 + A219652(A230429(n,k)) - A219652(A230428(n,k)).