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 A047355 Numbers that are congruent to {0, 3} mod 7. 13
 0, 3, 7, 10, 14, 17, 21, 24, 28, 31, 35, 38, 42, 45, 49, 52, 56, 59, 63, 66, 70, 73, 77, 80, 84, 87, 91, 94, 98, 101, 105, 108, 112, 115, 119, 122, 126, 129, 133, 136, 140, 143, 147, 150, 154, 157, 161, 164, 168, 171, 175, 178, 182, 185, 189, 192, 196, 199, 203 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Numbers k such that k^2/7 + k*(k + 1)/7 = k*(2*k + 1)/7 is a nonnegative integer. - Bruno Berselli, Feb 14 2017 LINKS David Lovler, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,1,-1). FORMULA a(n) = a(n-2) + 7 = a(n-1) + a(n-2) - a(n-3). - Henry Bottomley, Jan 19 2001 From Bruno Berselli, Sep 12 2011: (Start) G.f.: x^2*(3 + 4*x)/((1 + x)*(1 - x)^2). a(n) = (14*n - (-1)^n - 15)/4. (End) a(n+1) = Sum_{k>=0} A030308(n,k)*A125176(k+2). - Philippe Deléham, Oct 17 2011 a(n) = 2*n - 2 + floor((3*n - 3)/2). - Wesley Ivan Hurt, Jan 30 2014 E.g.f.: 4 + ((14*x - 15)*exp(x) - exp(-x))/4. - David Lovler, Aug 31 2022 MAPLE A047355:=n->(14*n - (-1)^n - 15)/4; seq(A047355(n), n=1..100); # Wesley Ivan Hurt, Jan 30 2014 MATHEMATICA Table[(14n - (-1)^n - 15)/4, {n, 100}] (* Wesley Ivan Hurt, Jan 30 2014 *) PROG (Haskell) a047355 n = a047355_list !! (n-1) a047355_list = scanl (+) 0 a010702_list -- Reinhard Zumkeller, Jul 05 2012 (PARI) a(n)=n\2*7 - 4 + n%2*4 \\ Charles R Greathouse IV, Aug 01 2016 CROSSREFS Cf. A030123, A010702 (first differences). Cf. A030308, A125176. Sequence in context: A288999 A310187 A198268 * A248522 A098005 A322533 Adjacent sequences: A047352 A047353 A047354 * A047356 A047357 A047358 KEYWORD nonn,easy AUTHOR N. J. A. Sloane STATUS approved

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Last modified July 12 16:16 EDT 2024. Contains 374251 sequences. (Running on oeis4.)