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A330983 Alternatively add and multiply pairs of the nonnegative integers.

%I A330983 #26 Feb 28 2020 13:50:07
%S A330983 1,6,9,42,17,110,25,210,33,342,41,506,49,702,57,930,65,1190,73,1482,
%T A330983 81,1806,89,2162,97,2550,105,2970,113,3422,121,3906,129,4422,137,4970,
%U A330983 145,5550,153,6162,161,6806,169,7482,177,8190,185,8930,193,9702,201,10506,209
%N A330983 Alternatively add and multiply pairs of the nonnegative integers.
%C A330983 In groups of two, add and multiply the integers: 0+1, 2*3, 4+5, 6*7, ....
%H A330983 Colin Barker, <a href="/A330983/b330983.txt">Table of n, a(n) for n = 1..1000</a>
%H A330983 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-3,0,1).
%F A330983 From _Colin Barker_, Jan 05 2020: (Start)
%F A330983 G.f.: x*(1 + 6*x + 6*x^2 + 24*x^3 - 7*x^4 + 2*x^5) / ((1 - x)^3*(1 + x)^3).
%F A330983 a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6) for n>6.
%F A330983 a(n) = (1/2)*(-1 + 5*(-1)^n - 2*(1 + 5*(-1)^n)*n + 4*(1+(-1)^n)*n^2).
%F A330983 (End)
%F A330983 E.g.f.: (2 + 4*x*(1 + x))*cosh(x) - (3 + 2*x)*sinh(x) - 2. - _Stefano Spezia_, Jan 05 2020 after _Colin Barker_
%t A330983 a[n_]:=If[OddQ[n],4n-3,2(n-1)(2n-1)]; Array[a,53] (* _Stefano Spezia_, Jan 05 2020 *)
%o A330983 (PARI) Vec(x*(1 + 6*x + 6*x^2 + 24*x^3 - 7*x^4 + 2*x^5) / ((1 - x)^3*(1 + x)^3) + O(x^50)) \\ _Colin Barker_, Jan 07 2020
%Y A330983 Cf. A330987.
%Y A330983 Interspersion of A017077 and A256833. - _Michel Marcus_, Jan 06 2020
%K A330983 nonn,easy
%O A330983 1,2
%A A330983 _George E. Antoniou_, Jan 05 2020