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A209971
a(n) = A000129(n) + n.
1
0, 2, 4, 8, 16, 34, 76, 176, 416, 994, 2388, 5752, 13872, 33474, 80796, 195040, 470848, 1136706, 2744228, 6625128, 15994448, 38613986, 93222380, 225058704, 543339744, 1311738146, 3166815988, 7645370072, 18457556080, 44560482178, 107578520380, 259717522880
OFFSET
0,2
REFERENCES
Paul Brickman, Problem in August 2011 issue of Fibonacci Quarterly. [Brickman has several problems in this issue, and I am not sure now which one I was referring to. - N. J. A. Sloane, Jan 22 2019]
FORMULA
G.f.: 2*x*(-1+2*x) / ( (x^2+2*x-1)*(x-1)^2 ). a(n) = 2*A100131(n-1). - R. J. Mathar, Mar 27 2012
From Colin Barker, Nov 06 2017: (Start)
a(n) = (-(1-sqrt(2))^n + (1+sqrt(2))^n) / (2*sqrt(2)) + n.
a(n) = 4*a(n-1) - 4*a(n-2) + a(n-4) for n>3.
(End)
PROG
(PARI) concat(0, Vec( 2*x*(1 - 2*x) / ((1 - x)^2*(1 - 2*x - x^2)) + O(x^50))) \\ Colin Barker, Nov 06 2017
CROSSREFS
Cf. A000129.
Sequence in context: A045648 A248890 A308245 * A308031 A166354 A336009
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Mar 25 2012
STATUS
approved