A079460 Let r(n) be the real positive root of Sum_{k=1..n} x^k = 1, then a(n) = round(1/(r(n) - 1/2)).

2, 8, 23, 53, 115, 242, 496, 1006, 2028, 4074, 8168, 16358, 32740, 65506, 131040, 262110, 524252, 1048538, 2097112, 4194262, 8388564, 16777170, 33554384, 67108814, 134217676, 268435402, 536870856, 1073741766, 2147483588

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Formula

For n >= 6, a(n) = 2^(n+2) - 2*(n+1).

G.f.: x*(2 + x^2 - 3*x^3 + 2*x^4 + x^5 - 3*x^6 + 2*x^7)/((1-x)^2*(1-2*x)). - Colin Barker, Dec 02 2012

Mathematica

LinearRecurrence[{4, -5, 2}, {2, 8, 23, 53, 115, 242, 496, 1006}, 30] (* Harvey P. Dale, Dec 15 2015 *)

Prog

(PARI) my(x='x+O('x^30)); Vec(x*(2+x^2-3*x^3+2*x^4+x^5-3*x^6+2*x^7 )/((1-x)^2*(1-2*x))) \\ G. C. Greubel, Jan 18 2019
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( x*(2+x^2-3*x^3+2*x^4+x^5-3*x^6+2*x^7 )/((1-x)^2*(1-2*x)) )); // G. C. Greubel, Jan 18 2019
(Sage) a=(x*(2+x^2-3*x^3+2*x^4+x^5-3*x^6+2*x^7 )/((1-x)^2*(1-2*x)) ).series(x, 30).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Jan 18 2019
(GAP) a:=[242, 496, 1006];; for n in [4..30] do a[n]:=4*a[n-1]-5*a[n-2] +2*a[n-3]; od; Concatenation([2, 8, 23, 53, 115], a); # G. C. Greubel, Jan 18 2019

Crossrefs

Sequence in context: A014285 A331756 A330152 * A154144 A255942 A355551

Adjacent sequences: A079457 A079458 A079459 * A079461 A079462 A079463

Keyword

nonn,easy

Author

Benoit Cloitre, Jan 12 2003

Status

approved