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 A095100 Integers n of the form 4k+3 for which all sums Sum_{i=1..u} J(i/n) (with u ranging from 1 to (n-1)) are nonnegative, where J(i/n) is Jacobi symbol of i and n. 9
 3, 7, 11, 15, 23, 27, 31, 35, 39, 47, 55, 59, 63, 71, 75, 79, 83, 87, 95, 103, 111, 119, 131, 135, 143, 151, 159, 167, 171, 175, 183, 191, 199, 215, 231, 239, 243, 251, 255, 263, 271, 279, 287, 295, 299, 303, 311, 319, 327, 335, 343, 351, 359, 363 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Integers whose Jacobi-vector forms a valid Motzkin-path. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 A. Karttunen and J. Moyer, C-program for computing the initial terms of this sequence MATHEMATICA isMotzkin[n_, k_] := Module[{s = 0, r = True}, Do[s += JacobiSymbol[i, n]; If[s < 0, r = False; Break[]], {i, 1, k}]; r]; A095100[n_] := Select[4*Range[0, n+1]+3, isMotzkin[#, Quotient[#, 2]] &]; A095100[90] (* Jean-François Alcover, Oct 08 2013, translated from Sage *) PROG (Sage) def A095100_list(n) :     def is_Motzkin(n, k):         s = 0         for i in (1..k) :             s += jacobi_symbol(i, n)             if s < 0 : return false         return true     return filter(lambda m: is_Motzkin(m, m//2), range(n+1)[3::4]) A095100_list(363) # Peter Luschny, Aug 08 2012 CROSSREFS a(n) = 4*A095274(n)+3.Subset: A095102. Complement of A095101 in A004767. Cf. A095090. Sequence in context: A246559 A246521 A160785 * A036994 A243115 A279106 Adjacent sequences:  A095097 A095098 A095099 * A095101 A095102 A095103 KEYWORD nonn AUTHOR Antti Karttunen and Jun 01 2004 STATUS approved

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Last modified December 11 10:48 EST 2018. Contains 318049 sequences. (Running on oeis4.)