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%I #48 Oct 25 2023 09:29:58
%S 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 25,65,27,70,29,75,31,80,33,85,35,90,37,95,39,100,41,105,43,110,45,
%U 115,47,120,49,125,51,130,53,135,55,140,57,145,59,150,61,155,63
%N Multiples of 5 and odd numbers interleaved.
%C This is 5*n/2 if n is even, n if n is odd.
%C Partial sums give the generalized enneagonal numbers A118277.
%C 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 Vincenzo Librandi, <a href="/A195140/b195140.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).
%F a(2n) = 5n, a(2n+1) = 2n+1.
%F G.f.: x*(1+5*x+x^2) / ((x-1)^2*(x+1)^2). - _Alois P. Heinz_, Sep 26 2011
%F From _Bruno Berselli_, Sep 27 2011: (Start)
%F a(n) = (7+3*(-1)^n)*n/4.
%F a(n) = -a(-n) = a(n-2)*n/(n-2) = 2*a(n-2)-a(n-4).
%F a(n) + a(n-1) = A047336(n). (End)
%F Multiplicative with a(2^e) = 5*2^(e-1), a(p^e) = p^e for odd prime p. - _Andrew Howroyd_, Jul 23 2018
%F Dirichlet g.f.: zeta(s-1) * (1 + 3/2^s). - _Amiram Eldar_, Oct 25 2023
%t 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 (Magma) &cat[[5*n,2*n+1]: n in [0..31]]; // _Bruno Berselli_, Sep 27 2011
%o (PARI) a(n)=(7+3*(-1)^n)*n/4 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A008587 and A005408 interleaved.
%Y Column 5 of A195151.
%Y 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 Cf. A047336, A118277.
%K nonn,easy,mult
%O 0,3
%A _Omar E. Pol_, Sep 10 2011
%E Corrected and edited by _Alois P. Heinz_, Sep 25 2011
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