A330983 Alternatively add and multiply pairs of the nonnegative integers.
1, 6, 9, 42, 17, 110, 25, 210, 33, 342, 41, 506, 49, 702, 57, 930, 65, 1190, 73, 1482, 81, 1806, 89, 2162, 97, 2550, 105, 2970, 113, 3422, 121, 3906, 129, 4422, 137, 4970, 145, 5550, 153, 6162, 161, 6806, 169, 7482, 177, 8190, 185, 8930, 193, 9702, 201, 10506, 209
Offset: 1
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).
Crossrefs
Cf. A330987.
Programs
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Mathematica
a[n_]:=If[OddQ[n],4n-3,2(n-1)(2n-1)]; Array[a,53] (* Stefano Spezia, Jan 05 2020 *)
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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
Formula
From Colin Barker, Jan 05 2020: (Start)
G.f.: x*(1 + 6*x + 6*x^2 + 24*x^3 - 7*x^4 + 2*x^5) / ((1 - x)^3*(1 + x)^3).
a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6) for n>6.
a(n) = (1/2)*(-1 + 5*(-1)^n - 2*(1 + 5*(-1)^n)*n + 4*(1+(-1)^n)*n^2).
(End)
E.g.f.: (2 + 4*x*(1 + x))*cosh(x) - (3 + 2*x)*sinh(x) - 2. - Stefano Spezia, Jan 05 2020 after Colin Barker
Comments