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A195035 Multiples of 15 and of 8 interleaved: a(2n-1) = 15n, a(2n) = 8n.

%I A195035 #36 Feb 16 2025 08:33:15
%S A195035 15,8,30,16,45,24,60,32,75,40,90,48,105,56,120,64,135,72,150,80,165,
%T A195035 88,180,96,195,104,210,112,225,120,240,128,255,136,270,144,285,152,
%U A195035 300,160,315,168,330,176,345,184,360,192,375,200,390,208,405,216
%N A195035 Multiples of 15 and of 8 interleaved: a(2n-1) = 15n, a(2n) = 8n.
%C A195035 First differences of A195036.
%C A195035 a(n) is also the length of the n-th edge of a square spiral in which the first two edges are the legs of the primitive Pythagorean triple [15, 8, 17]. Zero together with partial sums give A195036; the vertices of the spiral.
%H A195035 Vincenzo Librandi, <a href="/A195035/b195035.txt">Table of n, a(n) for n = 1..10000</a>
%H A195035 Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Pythag/pythag.html#uadgen">Pythagorean triangles and Triples</a>
%H A195035 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PythagoreanTriple.html">Pythagorean Triple</a>
%H A195035 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).
%F A195035 From _Bruno Berselli_, Sep 30 2011: (Start)
%F A195035 G.f.: x*(15+8*x)/((1-x)^2*(1+x)^2).
%F A195035 a(n) = A010686(n)*A010706(n-1)*A004526(n+1) = (23*n-(7*n+15)*(-1)^n+15)/4.
%F A195035 a(n) = 2*a(n-2) - a(n-4).
%F A195035 a(-n) = -a(A014681(n-1)). (End)
%t A195035 Riffle[15*#, 8*#] & [Range[50]] (* _Paolo Xausa_, Mar 21 2024 *)
%o A195035 (Magma) &cat[[15*n, 8*n]: n in [1..27]];  // _Bruno Berselli_, Sep 30 2011
%o A195035 (PARI) a(n)=(n+1)\2*if(n%2,15,8) \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A195035 Cf. A004526, A010686, A010706.
%Y A195035 Cf. A195019, A195031, A195033, A195036.
%K A195035 nonn,easy
%O A195035 1,1
%A A195035 _Omar E. Pol_, Sep 12 2011