This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A047215 #83 Jun 23 2025 10:47:48
%S A047215 0,2,5,7,10,12,15,17,20,22,25,27,30,32,35,37,40,42,45,47,50,52,55,57,
%T A047215 60,62,65,67,70,72,75,77,80,82,85,87,90,92,95,97,100,102,105,107,110,
%U A047215 112,115,117,120,122,125,127,130,132,135,137,140,142,145,147,150,152,155,157
%N A047215 Numbers that are congruent to {0, 2} mod 5.
%C A047215 Number of partitions of 5n into exactly 2 parts. - _Colin Barker_, Mar 23 2015
%C A047215 Numbers k such that k^2/5 + k*(k + 1)/5 = k*(2*k + 1)/5 is a nonnegative integer. - _Bruno Berselli_, Feb 14 2017
%H A047215 David Lovler, <a href="/A047215/b047215.txt">Table of n, a(n) for n = 0..1000</a>
%H A047215 Robbert Fokkink and Gandhar Joshi, <a href="https://arxiv.org/abs/2506.13337">Anti-recurrence sequences</a>, arXiv:2506.13337 [math.NT], 2025. See p. 4.
%H A047215 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A047215 a(n) = floor(5*n/2).
%F A047215 From _R. J. Mathar_, Sep 23 2008: (Start)
%F A047215 G.f.: x*(2 + 3*x)/((1 + x)*(1 - x)^2).
%F A047215 a(n) = 5*n/2 + ((-1)^n-1)/4.
%F A047215 a(n+1) - a(n) = A010693(n+1). (End)
%F A047215 a(n) = 5*n - a(n-1) - 8 with a(1)=0. - _Vincenzo Librandi_, Aug 05 2010
%F A047215 a(n+1) = Sum_{k>=0} A030308(n,k)*A084215(k+1). - _Philippe Deléham_, Oct 17 2011
%F A047215 a(n) = 2*n + floor(n/2). - _Arkadiusz Wesolowski_, Sep 19 2012
%F A047215 Sum_{n>=1} (-1)^(n+1)/a(n) = log(5)/4 - sqrt(5)*log(phi)/10 + sqrt(1-2/sqrt(5))*Pi/10, where phi is the golden ratio (A001622). - _Amiram Eldar_, Dec 07 2021
%F A047215 E.g.f.: (5*x*exp(x) - sinh(x))/2. - _David Lovler_, Aug 22 2022
%t A047215 Table[Floor[5 n/2], {n, 0, 100}] (* or *) LinearRecurrence[{1, 1, -1}, {0, 2, 5},101] (* _Vladimir Joseph Stephan Orlovsky_, Jan 28 2012 *)
%o A047215 (PARI) a(n)=5*n\2 \\ _Charles R Greathouse IV_, Oct 17 2011
%o A047215 (Magma) [(5*n - (n mod 2))/2: n in [1..100]]; // _G. C. Greubel_, Jun 23 2024
%o A047215 (SageMath) [int(5*n//2) for n in range(1,101)] # _G. C. Greubel_, Jun 23 2024
%Y A047215 Different from A038126.
%Y A047215 Cf. A001622, A010693, A030308, A084215
%Y A047215 Cf. A249547 (partial sums), A010693 (1st differences).
%K A047215 nonn,easy
%O A047215 0,2
%A A047215 _N. J. A. Sloane_