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 A047352 Numbers that are congruent to {0, 2} mod 7. 7
 0, 2, 7, 9, 14, 16, 21, 23, 28, 30, 35, 37, 42, 44, 49, 51, 56, 58, 63, 65, 70, 72, 77, 79, 84, 86, 91, 93, 98, 100, 105, 107, 112, 114, 119, 121, 126, 128, 133, 135, 140, 142, 147, 149, 154, 156, 161, 163, 168, 170 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Numbers k such that k^2/7 + k*(k + 1)/14 = k*(3*k + 1)/14 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) = 7*n - a(n-1) - 12 with a(1)=0. Also: a(n) = a(n-1) + a(n-2) - a(n-3). - Vincenzo Librandi, Aug 05 2010 a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=2 and b(k)=A005009(k-1) for k>0. - Philippe Deléham, Oct 17 2011 G.f.: x^2*(2 + 5*x)/((1 + x)*(1 - x)^2). - R. J. Mathar, Dec 04 2011 a(n) = floor((7/3)*floor(3*n/2)). - Clark Kimberling, Jul 04 2012 E.g.f.: 5 + ((14*x - 17)*exp(x) - 3*exp(-x))/4. - David Lovler, Aug 31 2022 MATHEMATICA LinearRecurrence[{1, 1, -1}, {0, 2, 7}, 50] (* Harvey P. Dale, Oct 16 2022 *) PROG (PARI) forstep(n=0, 200, [2, 5], print1(n", ")) \\ Charles R Greathouse IV, Oct 17 2011 CROSSREFS Cf. A005009, A030308. Sequence in context: A077470 A347370 A205559 * A184400 A074244 A190565 Adjacent sequences: A047349 A047350 A047351 * A047353 A047354 A047355 KEYWORD nonn,easy AUTHOR N. J. A. Sloane STATUS approved

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Last modified July 14 05:06 EDT 2024. Contains 374291 sequences. (Running on oeis4.)