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 A016921 a(n) = 6n + 1. 91
 1, 7, 13, 19, 25, 31, 37, 43, 49, 55, 61, 67, 73, 79, 85, 91, 97, 103, 109, 115, 121, 127, 133, 139, 145, 151, 157, 163, 169, 175, 181, 187, 193, 199, 205, 211, 217, 223, 229, 235, 241, 247, 253, 259, 265, 271, 277, 283, 289, 295, 301, 307, 313, 319, 325, 331 (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( 22 ). Also solutions to 2^x + 3^x == 5 (mod 7). - Cino Hilliard, May 10 2003 Except for 1, exponents n > 1 such that x^n - x^2 - 1 is reducible. - N. J. A. Sloane, Jul 19 2005 Let M(n) be the n X n matrix m(i,j) = min(i,j); then the trace of M(n)^(-2) is a(n-1) = 6*n - 5. - Benoit Cloitre, Feb 09 2006 If Y is a 3-subset of an (2n+1)-set X then, for n >= 3, a(n-1) is the number of 3-subsets of X having at least two elements in common with Y. - Milan Janjic, Dec 16 2007 A008615(a(n)) = n. - Reinhard Zumkeller, Feb 27 2008 A157176(a(n)) = A013730(n). - Reinhard Zumkeller, Feb 24 2009 All composite terms belong to A269345 as shown in there. - Waldemar Puszkarz, Apr 13 2016 First differences of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 773", based on the 5-celled von Neumann neighborhood. - Robert Price, May 23 2016 For b(n) = A103221(n) one has b(a(n)-1) = b(a(n)+1) = b(a(n)+2) = b(a(n)+3) = b(a(n)+4) = n+1 but b(a(n)) = n. So-called "dips" in A103221. See the Avner and Gross remark on p. 178. - Wolfdieter Lang, Sep 16 2016 REFERENCES Avner Ash and Robert Gross, Summing it up, Princeton University Press, 2016, p. 178. LINKS Tanya Khovanova, Recursive Sequences William A. Stein, Dimensions of the spaces S_k(Gamma_0(N)) William A. Stein, The modular forms database Index entries for linear recurrences with constant coefficients, signature (2,-1). FORMULA a(n) = 6*n + 1, n >= 0 (see the name). G.f.: (1+5*x)/(1-x)^2. a(n) = 4*(3*n-1) - a(n-1) (with a(0)=1). - Vincenzo Librandi, Nov 20 2010 EXAMPLE From Ilya Gutkovskiy, Apr 15 2016: (Start) Illustration of initial terms:                       o                     o o o               o     o o o             o o o   o o o       o     o o o   o o o     o o o   o o o   o o o o   o o o   o o o   o o o n=0  n=1     n=2     n=3 (End) MAPLE a[1]:=1:for n from 2 to 100 do a[n]:=a[n-1]+6 od: seq(a[n], n=1..56); # Zerinvary Lajos, Mar 16 2008 MATHEMATICA Range[1, 500, 6] (* Vladimir Joseph Stephan Orlovsky, May 26 2011 *) PROG (Sage) [i+1 for i in range(333) if gcd(i, 6) == 6] # Zerinvary Lajos, May 20 2009 (Haskell) a016921 = (+ 1) . (* 6) a016921_list = [1, 7 ..]  -- Reinhard Zumkeller, Jan 15 2013 (PARI) a(n)=6*n+1 \\ Charles R Greathouse IV, Mar 22 2016 (Python) for n in xrange(0, 10**5):print(6*n+1) # Soumil Mandal, Apr 14 2016 CROSSREFS Cf. A093563 ((6, 1) Pascal, column m=1). Cf. A008588, A016933, A016945, A016957, A161700, A005408, A016813, A017281, A017533, A158057, A161705, A161709, A161714, A128470, A002476 (primes), A000567 (partial sums). a(n)=A007310(2*(n+1)); complement of A016969 with respect to A007310. Cf. A287326 (second column). Sequence in context: A059335 A070419 A080199 * A260682 A184521 A123843 Adjacent sequences:  A016918 A016919 A016920 * A016922 A016923 A016924 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified November 19 19:37 EST 2018. Contains 317364 sequences. (Running on oeis4.)