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 A062318 Numbers of the form 3^m - 1 or 2*3^m - 1; i.e., the union of sequences A048473 and A024023. 39
 0, 1, 2, 5, 8, 17, 26, 53, 80, 161, 242, 485, 728, 1457, 2186, 4373, 6560, 13121, 19682, 39365, 59048, 118097, 177146, 354293, 531440, 1062881, 1594322, 3188645, 4782968, 9565937, 14348906, 28697813, 43046720, 86093441, 129140162 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS WARNING: The offset of this sequence has been changed from 0 to 1 without correcting the formulas and programs, many of them correspond to the original indexing a(0)=0, a(1)=1, ... - M. F. Hasler, Oct 06 2014 Numbers n such that no entry in n-th row of Pascal's triangle is divisible by 3, i.e., such that A062296(n) = 0. The base 3 representation of these numbers is 222...222 or 122...222. a(n+1) is the smallest number with ternary digit sum = n: A053735(a(n+1)) = n and A053735(m) <> n for m < a(n+1). - Reinhard Zumkeller, Sep 15 2006 A138002(a(n)) = 0. - Reinhard Zumkeller, Feb 26 2008 Also, number of terms in S(n), where S(n) is defined in A114482. - N. J. A. Sloane, Nov 13 2014 a(n+1) is also the Moore lower bound on the order of a (4,g)-cage. - Jason Kimberley, Oct 30 2011 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Gy. Tasi and F. Mizukami, Quantum algebraic-combinatoric study of the conformational properties of n-alkanes, J. Math. Chemistry, 25, 1999, 55-64 (see p. 60). Index entries for linear recurrences with constant coefficients, signature (1,3,-3). FORMULA a(n) = 2*3^(n/2-1)-1 if n is even; a(n) = 3^(n/2-1/2)-1 if n is odd. - Emeric Deutsch, Feb 03 2005, offset updated a(n) = a(n-1)+3*a(n-2)-3*a(n-3). Differences: A108411. - Paul Curtz, Feb 21 2008 G.f.: x^2*(1+x)/((1-x)*(1-3*x^2)). - Colin Barker, Apr 02 2012 a(2n+1) = 3*a(2n-1) + 2;  a(2n) = ( a(2n-1) + a(2n+1) )/2. See A060647 for case where a(1)= 1. - Richard R. Forberg, Nov 30 2013 a(n) = 2^((1+(-1)^n)/2) * 3^((2*n-3-(-1)^n)/4) - 1. - Luce ETIENNE, Aug 29 2014 EXAMPLE The first rows in Pascal's triangle with no multiples of 3 are: row 0: 1; row 1: 1,1; row 2: 1,2,1; row 5: 1,5,10,10,5,1; row 8: 1,8,28,56,70,56,28,8,1; MAPLE A062318 :=proc(n)     if n mod 2 = 1 then         3^((n-1)/2)-1     else         2*3^(n/2-1)-1     fi end proc: seq(A062318(n), n=1..37); # Emeric Deutsch, Feb 03 2005, offset updated MATHEMATICA CoefficientList[Series[x^2*(1+x)/((1-x)*(1-3*x^2)), {x, 0, 40}], x] (* Vincenzo Librandi, Apr 20 2012 *) PROG (MAGMA) I:=[0, 1, 2]; [n le 3 select I[n] else Self(n-1)+3*Self(n-2)-3*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Apr 20 2012 (PARI) a(n)=3^(n\2)<

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Last modified December 11 22:04 EST 2018. Contains 318052 sequences. (Running on oeis4.)