A330983 - OEIS

%I #26 Feb 28 2020 13:50:07

%S 1,6,9,42,17,110,25,210,33,342,41,506,49,702,57,930,65,1190,73,1482,

%T 81,1806,89,2162,97,2550,105,2970,113,3422,121,3906,129,4422,137,4970,

%U 145,5550,153,6162,161,6806,169,7482,177,8190,185,8930,193,9702,201,10506,209

%N Alternatively add and multiply pairs of the nonnegative integers.

%C In groups of two, add and multiply the integers: 0+1, 2*3, 4+5, 6*7, ....

%H Colin Barker, <a href="/A330983/b330983.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-3,0,1).

%F From _Colin Barker_, Jan 05 2020: (Start)

%F 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 a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6) for n>6.

%F a(n) = (1/2)*(-1 + 5*(-1)^n - 2*(1 + 5*(-1)^n)*n + 4*(1+(-1)^n)*n^2).

%F (End)

%F 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 a[n_]:=If[OddQ[n],4n-3,2(n-1)(2n-1)]; Array[a,53] (* _Stefano Spezia_, Jan 05 2020 *)

%o (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 Cf. A330987.

%Y Interspersion of A017077 and A256833. - _Michel Marcus_, Jan 06 2020

%K nonn,easy

%O 1,2

%A _George E. Antoniou_, Jan 05 2020