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A268444
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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.
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3
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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
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0,2
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COMMENTS
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a(n) gives the number of 1's in row n of A243756.
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LINKS
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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.
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FORMULA
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a(n) = Product_{i=0..k}(n_i+1) where n = Sum_{i=0..k}n_i*4^i.
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EXAMPLE
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The base-4 representation of 10 is (2,2) so a(10) = (2+1)*(2+1) = 9.
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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