A081663 a(n) = Fibonacci(2n+1) + n*2^(n-1).

1, 3, 9, 25, 66, 169, 425, 1058, 2621, 6485, 16066, 39921, 99601, 249666, 628917, 1592029, 4048866, 10341577, 26517113, 68226722, 176065901, 455514533, 1181040514, 3067684065, 7980068641, 20784441474, 54188706405, 141395801773

Offset: 0

Author

Paul Barry, Mar 26 2003

Keywords

• easy
• nonn

Comments

Binomial transform of n + Fibonacci(n+1), A081659.

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-17,16,-4).

Crossrefs

Cf. A000045, A001519, A001787, A081659.

Programs

Mathematica

Table[Fibonacci[2n+1]+n 2^(n-1),{n,0,30}] (* or *) LinearRecurrence[{7,-17,16,-4},{1,3,9,25},30] (* Harvey P. Dale, Sep 17 2020 *)

Formula

a(n) = A001519(n)+A001787(n).

a(n) = 7*a(n-1)-17*a(n-2)+16*a(n-3)-4*a(n-4). G.f.: -(3*x^3-5*x^2+4*x-1) / ((2*x-1)^2*(x^2-3*x+1)). - Colin Barker, Jun 04 2013

Extensions

Definition corrected by Matt Lehman, May 21 2010