

A268444


a(n) = Product_{i=0..k}(n_i+1) where n = Sum_{i=0..k}n_i*4^i is the base4 representation of n.


3



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
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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. 135143.


FORMULA

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


EXAMPLE

The base4 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



