cp's OEIS Frontend

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.

%I A268444 #25 Apr 24 2025 13:20:59
%S A268444 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,
%T A268444 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,
%U A268444 32,12,24,36,48,16,32,48,64,2,4,6,8,4,8,12,16,6,12,18,24
%N 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.
%C A268444 a(n) gives the number of 1's in row n of A243756.
%H A268444 Antti Karttunen, <a href="/A268444/b268444.txt">Table of n, a(n) for n = 0..16384</a>
%H A268444 Tyler Ball, Tom Edgar, and Daniel Juda, <a href="http://dx.doi.org/10.4169/math.mag.87.2.135">Dominance Orders, Generalized Binomial Coefficients, and Kummer's Theorem</a>, Mathematics Magazine, Vol. 87, No. 2, April 2014, pp. 135-143.
%F A268444 a(n) = Product_{i=0..k}(n_i+1) where n = Sum_{i=0..k}n_i*4^i.
%e A268444 The base-4 representation of 10 is (2,2) so a(10) = (2+1)*(2+1) = 9.
%o A268444 (Sage) [prod(x+1 for x in n.digits(4)) for n in [0..75]]
%o A268444 (PARI) a(n) = my(d=digits(n,4)); prod(k=1, #d, d[k]+1); \\ _Michel Marcus_, Feb 05 2016
%o A268444 (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
%o A268444 (Python)
%o A268444 from math import prod
%o A268444 from gmpy2 import digits
%o A268444 def A268444(n):
%o A268444     s = digits(n,4)
%o A268444     return prod((int(d)+1)**s.count(d) for d in '123') # _Chai Wah Wu_, Apr 24 2025
%Y A268444 Cf. A001316, A006047, A074848.
%K A268444 nonn,base
%O A268444 0,2
%A A268444 _Tom Edgar_, Feb 04 2016