A268444 a(n) = Product_{i=0..k}(n_i+1) where n = Sum_{i=0..k}n_i*4^i is the base-4 representation of n.

1, 2, 3, 4, 2, 4, 6, 8, 3, 6, 9, 12, 4, 8, 12, 16, 2, 4, 6, 8, 4, 8, 12, 16, 6, 12, 18, 24, 8, 16, 24, 32, 3, 6, 9, 12, 6, 12, 18, 24, 9, 18, 27, 36, 12, 24, 36, 48, 4, 8, 12, 16, 8, 16, 24, 32, 12, 24, 36, 48, 16, 32, 48, 64, 2, 4, 6, 8, 4, 8, 12, 16, 6, 12, 18, 24

Offset

0,2

Comments

a(n) gives the number of 1's in row n of A243756.

Links

Antti Karttunen, Table of n, a(n) for n = 0..16384

Tyler Ball, Tom Edgar, and Daniel Juda, Dominance Orders, Generalized Binomial Coefficients, and Kummer's Theorem, Mathematics Magazine, Vol. 87, No. 2, April 2014, pp. 135-143.

Formula

a(n) = Product_{i=0..k}(n_i+1) where n = Sum_{i=0..k}n_i*4^i.

Example

The base-4 representation of 10 is (2,2) so a(10) = (2+1)*(2+1) = 9.

Prog

(Sage) [prod(x+1 for x in n.digits(4)) for n in [0..75]]
(PARI) a(n) = my(d=digits(n, 4)); prod(k=1, #d, d[k]+1); \\ Michel Marcus, Feb 05 2016
(Scheme) (define (A268444 n) (if (zero? n) 1 (let ((d (mod n 4))) (* (+ 1 d) (A268444 (/ (- n d) 4)))))) ;; For R6RS standard. Use modulo instead of mod in older Schemes like MIT/GNU Scheme. - Antti Karttunen, May 28 2017

Crossrefs

Cf. A001316, A006047, A074848.

Sequence in context: A338272 A107572 A043264 * A117826 A322604 A173229

Adjacent sequences: A268441 A268442 A268443 * A268445 A268446 A268447

Keyword

nonn,base

Author

Tom Edgar, Feb 04 2016

Status

approved