A054146 a(n) = A054145(n)/2.

0, 1, 6, 29, 128, 536, 2168, 8556, 33152, 126640, 478304, 1789840, 6646272, 24519680, 89956224, 328437184, 1194102784, 4325299456, 15615510016, 56209986816, 201798074368, 722731821056, 2582790830080, 9211619462144

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8,-20,16,-4).

Formula

From G. C. Greubel, Aug 01 2019: (Start)

a(n) = ((n-2)*((2 + sqrt(2))^n + (2 - sqrt(2))^n) + sqrt(2)*((2 + sqrt(2))^n - (2 - sqrt(2))^n))/16.

G.f.: x*(1 - x)^2/(1 - 4*x + 2*x^2)^2. (End)

Mathematica

LinearRecurrence[{8, -20, 16, -4}, {0, 1, 6, 29}, 30] (* G. C. Greubel, Aug 01 2019 *)

Prog

(PARI) my(x='x+O('x^30)); concat([0], Vec(x*(1-x)^2/(1-4*x+2*x^2)^2)) \\ G. C. Greubel, Aug 01 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); [0] cat Coefficients(R!( x*(1-x)^2/(1-4*x+2*x^2)^2 )); // G. C. Greubel, Aug 01 2019
(Sage) (x*(1-x)^2/(1-4*x+2*x^2)^2).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Aug 01 2019
(GAP) a:=[0, 1, 6, 29];; for n in [5..30] do a[n]:=8*a[n-1]-20*a[n-2] +16*a[n-3]-4*a[n-4]; od; a; # G. C. Greubel, Aug 01 2019

Crossrefs

Cf. A054144, A054145.

Sequence in context: A111644 A225618 A081278 * A172062 A081674 A173413

Adjacent sequences: A054143 A054144 A054145 * A054147 A054148 A054149

Keyword

nonn

Author

Clark Kimberling, Mar 18 2000

Status

approved