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 A195140 #48 Oct 25 2023 09:29:58
%S A195140 0,1,5,3,10,5,15,7,20,9,25,11,30,13,35,15,40,17,45,19,50,21,55,23,60,
%T A195140 25,65,27,70,29,75,31,80,33,85,35,90,37,95,39,100,41,105,43,110,45,
%U A195140 115,47,120,49,125,51,130,53,135,55,140,57,145,59,150,61,155,63
%N A195140 Multiples of 5 and odd numbers interleaved.
%C A195140 This is 5*n/2 if n is even, n if n is odd.
%C A195140 Partial sums give the generalized enneagonal numbers A118277.
%C A195140 a(n) is also the length of the n-th line segment of a rectangular spiral on the infinite square grid. The vertices of the spiral are the generalized enneagonal numbers. - _Omar E. Pol_, Jul 27 2018
%H A195140 Vincenzo Librandi, <a href="/A195140/b195140.txt">Table of n, a(n) for n = 0..10000</a>
%H A195140 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).
%F A195140 a(2n) = 5n, a(2n+1) = 2n+1.
%F A195140 G.f.: x*(1+5*x+x^2) / ((x-1)^2*(x+1)^2). - _Alois P. Heinz_, Sep 26 2011
%F A195140 From _Bruno Berselli_, Sep 27 2011: (Start)
%F A195140 a(n) = (7+3*(-1)^n)*n/4.
%F A195140 a(n) = -a(-n) = a(n-2)*n/(n-2) = 2*a(n-2)-a(n-4).
%F A195140 a(n) + a(n-1) = A047336(n). (End)
%F A195140 Multiplicative with a(2^e) = 5*2^(e-1), a(p^e) = p^e for odd prime p. - _Andrew Howroyd_, Jul 23 2018
%F A195140 Dirichlet g.f.: zeta(s-1) * (1 + 3/2^s). - _Amiram Eldar_, Oct 25 2023
%t A195140 With[{nn=40},Riffle[5*Range[0,nn],Range[1,2nn+1,2]]] (* or *) LinearRecurrence[ {0,2,0,-1},{0,1,5,3},80] (* _Harvey P. Dale_, Dec 15 2014 *)
%o A195140 (Magma) &cat[[5*n,2*n+1]: n in [0..31]]; // _Bruno Berselli_, Sep 27 2011
%o A195140 (PARI) a(n)=(7+3*(-1)^n)*n/4 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A195140 A008587 and A005408 interleaved.
%Y A195140 Column 5 of A195151.
%Y A195140 Cf. Sequences whose partial sums give the generalized n-gonal numbers, if n>=5: A026741, A001477, zero together with A080512, A022998, this sequence, zero together with A165998, A195159, A195161, A195312.
%Y A195140 Cf. A047336, A118277.
%K A195140 nonn,easy,mult
%O A195140 0,3
%A A195140 _Omar E. Pol_, Sep 10 2011
%E A195140 Corrected and edited by _Alois P. Heinz_, Sep 25 2011