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 A195817 #37 Oct 24 2024 01:25:52
%S A195817 0,1,10,3,20,5,30,7,40,9,50,11,60,13,70,15,80,17,90,19,100,21,110,23,
%T A195817 120,25,130,27,140,29,150,31,160,33,170,35,180,37,190,39,200,41,210,
%U A195817 43,220,45,230,47,240,49,250,51,260,53,270,55,280,57,290,59,300
%N A195817 Multiples of 10 and odd numbers interleaved.
%C A195817 A008592 and A005408 interleaved.
%C A195817 Partial sums give the generalized 14-gonal (or tetradecagonal) numbers A195818.
%C A195817 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 14-gonal numbers. - _Omar E. Pol_, Jul 27 2018
%H A195817 Vincenzo Librandi, <a href="/A195817/b195817.txt">Table of n, a(n) for n = 0..10000</a>
%H A195817 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).
%F A195817 a(n) = (2*(-1)^n+3)*n. - _Vincenzo Librandi_, Sep 30 2011
%F A195817 From _Bruno Berselli_, Sep 30 2011: (Start)
%F A195817 G.f.: x*(1+10*x+x^2)/((1-x)^2*(1+x)^2).
%F A195817 a(n) = -a(-n) = a(n-2)*n/(n-2) = 2*a(n-2)-a(n-4).
%F A195817 a(n) * a(n+1) = a(n(n+1)).
%F A195817 a(n) + a(n+1) = A091998(n+1). (End)
%F A195817 a(0)=0, a(1)=1, a(2)=10, a(3)=3, a(n)=2*a(n-2)-a(n-4). - _Harvey P. Dale_, Nov 24 2013
%F A195817 Multiplicative with a(2^e) = 5*2^e, a(p^e) = p^e for odd prime p. - _Andrew Howroyd_, Jul 23 2018
%F A195817 Dirichlet g.f.: zeta(s-1) * (1 + 2^(3-s)). - _Amiram Eldar_, Oct 25 2023
%t A195817 With[{nn=30},Riffle[10*Range[0,nn],Range[1,2*nn+1,2]]] (* or *) LinearRecurrence[{0,2,0,-1},{0,1,10,3},70] (* _Harvey P. Dale_, Nov 24 2013 *)
%o A195817 (Magma) [(2*(-1)^n+3)*n: n in [0..60]]; // _Vincenzo Librandi_, Sep 30 2011
%o A195817 (PARI) a(n) = (2*(-1)^n+3)*n; \\ _Andrew Howroyd_, Jul 23 2018
%Y A195817 Column 10 of A195151.
%Y A195817 Sequences whose partial sums give the generalized n-gonal numbers, if n>=5: A026741, A001477, zero together with A080512, A022998, A195140, zero together with A165998, A195159, A195161, A195312, this sequence.
%Y A195817 Cf. A091998, A195152.
%K A195817 nonn,easy,mult
%O A195817 0,3
%A A195817 _Omar E. Pol_, Sep 29 2011