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 A008586 Multiples of 4. 143
 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 180, 184, 188, 192, 196, 200, 204, 208, 212, 216, 220, 224, 228 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 14 ). A000466(n), A008586(n) and A053755(n) are Pythagorean triples. - Zak Seidov, Jan 16 2007 If X is an n-set and Y and Z disjoint 2-subsets of X then a(n-3) is equal to the number of 3-subsets of X intersecting both Y and Z. - Milan Janjic, Aug 26 2007 Number of n permutations (n>=1) of 5 objects u, v, z, x, y with repetition allowed, containing n-1 u's. Example: if n=1 then n-1 =zero (0) u, a(1)=4 because we have v, z, x, y. If n=2 then n-1= one (1) u, a(2)=8 because we have vu, zu, xu, yu, uv, uz, ux, uy. A038231 formatted as a triangular array: diagonal :4,8,12,16,20,24,28,32... [Zerinvary Lajos, Aug 06 2008] For n > 0: numbers having more even than odd divisors: A048272(a(n)) < 0. [Reinhard Zumkeller, Jan 21 2012] A214546(a(n)) < 0 for n > 0. - Reinhard Zumkeller, Jul 20 2012 A090418(a(n)) = 0 for n > 0. - Reinhard Zumkeller, Aug 06 2012 Terms are the differences of consecutive centered square numbers (A001844). - Mihir Mathur, Apr 02 2013 a(n)*Pi = nonnegative zeros of the cycloid generated by a circle of radius 2 rolling along the positive x-axis from zero. [Wesley Ivan Hurt, Jul 01 2013] Apart from the initial term, number of vertices of minimal path on a n-dimensional cubic lattice (n>1) of side length 2, until a self-avoiding walk gets stuck.  A004767 + 1. - Matthew Lehman, Dec 23 2013 The number of orbits of Aut(Z^7) as function of the infinity norm n of the representative lattice point of the orbit, when the cardinality of the orbit is equal to 2688. - Philippe A.J.G. Chevalier, Dec 29 2015 First differences of A001844. - Robert Price, May 13 2016 Numbers k such that Fibonacci(k) is a multiple of 3 (A033888). - Bruno Berselli, Oct 17 2017 REFERENCES T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 3. LINKS T. D. Noe, Table of n, a(n) for n = 0..1000 Milan Janjic, Two Enumerative Functions Tanya Khovanova, Recursive Sequences INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 316 Franck Ramaharo, Statistics on some classes of knot shadows, arXiv:1802.07701 [math.CO], 2018. Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014, 2015. William A. Stein, The modular forms database Eric Weisstein's World of Mathematics, Doubly Even Number Index entries for linear recurrences with constant coefficients, signature (2,-1). FORMULA a(n) = A008574(n), n>0. - R. J. Mathar, Oct 28 2008 a(n) = Sum_k>=0 {A030308(n,k)*2^(k+2)}. - Philippe Deléham, Oct 17 2011 a(n+1) = A000290(n+2) - A000290(n). - Philippe Deléham, Mar 31 2013 G.f.: 4*x/(1-x)^2. - David Wilding, Jun 21 2014 MAPLE A008586:=n->4*n; seq(A008586(n), n=0..100); # Wesley Ivan Hurt, Feb 24 2014 MATHEMATICA Range[0, 500, 4] (* Vladimir Joseph Stephan Orlovsky, May 26 2011 *) PROG (PARI) a(n)=n<<2 \\ Charles R Greathouse IV, Oct 17 2011 (Haskell) a008586 = (* 4) a008586_list = [0, 4 ..]  -- Reinhard Zumkeller, May 13 2014 CROSSREFS Cf. A038231, A035008, A004767. Number of orbits of Aut(Z^7) as function of the infinity norm A000579, A154286, A102860, A002412, A045943, A115067, A008585, A005843, A001477, A000217. Sequence in context: A076310 A161352 A295774 * A059558 A008574 A189917 Adjacent sequences:  A008583 A008584 A008585 * A008587 A008588 A008589 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified July 20 15:59 EDT 2019. Contains 325185 sequences. (Running on oeis4.)