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

1,4

Comments

See A007623 for the factorial number system representation.

Links

Table of n, a(n) for n=1..55.

Formula

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

Example

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.

Prog

(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)))))))

Crossrefs

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

Sequence in context: A125278 A134558 A344639 * A137381 A109316 A162980

Adjacent sequences: A230417 A230418 A230419 * A230421 A230422 A230423

Keyword

nonn,base,tabl

Author

Antti Karttunen, Oct 18 2013

Status

approved