A276226 a(n+3) = 2*a(n+2) + a(n+1) + a(n) with a(0)=0, a(1)=6, a(2)=8.

0, 6, 8, 22, 58, 146, 372, 948, 2414, 6148, 15658, 39878, 101562, 258660, 658760, 1677742, 4272904, 10882310, 27715266, 70585746, 179769068, 457839148, 1166033110, 2969674436, 7563221130, 19262149806, 49057195178, 124939761292, 318198867568, 810394691606, 2063928012072, 5256449583318, 13387221870314, 34094821336018

Offset: 0

Author

G. C. Greubel, Aug 24 2016

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (2,1,1).

Crossrefs

Cf. A276225, A077939.

Programs

Magma

I:=[0,6,8]; [n le 3 select I[n] else 2*Self(n-1)+ Self(n-2)+Self(n-3): n in [1..40]]; // Vincenzo Librandi, Aug 25 2016

Mathematica

LinearRecurrence[{2, 1, 1}, {0, 6, 8}, 50]
CoefficientList[Series[2 (3 x - 2 x^2)/(1 - 2 x - x^2 - x^3), {x, 0, 33}], x] (* Michael De Vlieger, Aug 25 2016 *)

PARI

concat(0, Vec(2*(3*x-2*x^2)/(1-2*x-x^2-x^3) + O(x^99))) \\ Altug Alkan, Aug 25 2016

Formula

Let p = (4*(61 + 9*sqrt(29)))^(1/3), q = (4*(61 - 9*sqrt(29)))^(1/3), and x = (1/6)*(4 + p + q) then x^n = (1/6)*(2*A276225(n) + a(n)*(p + q) + A077939(n-1)*(p^2 + q^2)).G.f.: 2*(3*x - 2*x^2)/(1 - 2*x - x^2 - x^3).