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 A186034 2-adic valuation of the n-th Motzkin number. 2
 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 1, 2, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 2, 1, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 1, 2, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 1, 2, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Antti Karttunen, Table of n, a(n) for n = 0..4095 E. Rowland and R. Yassawi, Automatic congruences for diagonals of rational functions, arXiv preprint arXiv:1310.8635 [math.NT], 2013-2014. FORMULA a(n) = log_2(A001006(n)/numerator(A001006(n)/2^n)). (-1)^a(n) = A186035(n). a(n) = A007814(A001006(n)). - Antti Karttunen, Aug 12 2017 MAPLE A186034 := proc(n) local m, ml ; m := A001006(n) ; ml := %/2^n ; m/numer(ml) ; ilog2(%) ; end proc: seq(A186034(n), n=0..80) ; # R. J. Mathar, Feb 13 2015 MATHEMATICA IntegerExponent[RecurrenceTable[(n + 4) M[n + 2] - (2 n + 5) M[n + 1] - 3 (n + 1) M[n] == 0 && M[0] == M[1] == 1, M[n], {n, 0, 127}], 2] (* Eric Rowland, May 06 2013 *) PROG (Python) from itertools import count, islice def A186034_gen(): # generator of terms a, b = 1, 1 yield from (0, 0) for n in count(2): a, b = b, (b*(2*n+1)+a*3*(n-1))//(n+2) yield (~b&b-1).bit_length() A186034_list = list(islice(A186034_gen(), 30)) # Chai Wah Wu, Jul 08 2022 CROSSREFS Cf. A001006, A007814, A186035. Sequence in context: A103270 A087780 A082523 * A280843 A221146 A083935 Adjacent sequences: A186031 A186032 A186033 * A186035 A186036 A186037 KEYWORD nonn AUTHOR Paul Barry, Feb 11 2011 EXTENSIONS Definition edited by Eric Rowland, May 06 2013 More terms from Antti Karttunen, Aug 12 2017 STATUS approved

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Last modified March 21 19:39 EDT 2023. Contains 361410 sequences. (Running on oeis4.)