A140313 First differences of A140298.

1, 0, 0, 1, 1, 1, 1, 4, 4, 1, 13, 13, 1, 40, 40, 1, 121, 121, 1, 364, 364, 1, 1093, 1093, 1, 3280, 3280, 1, 9841, 9841, 1, 29524, 29524, 1, 88573, 88573, 1, 265720, 265720, 1, 797161, 797161, 1, 2391484, 2391484, 1, 7174453, 7174453, 1, 21523360, 21523360, 1, 64570081

Offset

0,8

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Formula

Mix 1, A003462(n), A003462(n).

G.f.: (x - 1)*(x^3 + 3*x^2 + 2*x + 1)/((3*x^3 - 1)*(x^2 + x + 1)). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009

Mathematica

CoefficientList[Series[(x - 1) (x^3 + 3 x^2 + 2 x + 1)/((3 x^3 - 1) (x^2 + x + 1)), {x, 0, 52}], x] (* Michael De Vlieger, Nov 05 2018 *)

Prog

(PARI) Vec((1 - x)*(1 + 2*x + 3*x^2 + x^3)/((1 - 3*x^3)*(1 + x + x^2)) + O(x^40)) \\ Andrew Howroyd, Nov 03 2018
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (x-1)*(x^3+3*x^2+2*x+1)/((3*x^3-1)*(x^2+x+1)) )); // G. C. Greubel, Nov 21 2018
(Sage) s=((x-1)*(x^3+3*x^2+2*x+1)/((3*x^3-1)*(x^2+x+1))).series(x, 50);
s.coefficients(x, sparse=False) # G. C. Greubel, Nov 21 2018

Crossrefs

Cf. A140298

Sequence in context: A365674 A106026 A096078 * A102323 A145902 A124028

Adjacent sequences: A140310 A140311 A140312 * A140314 A140315 A140316

Keyword

nonn

Author

Paul Curtz, May 25 2008

Extensions

Terms a(33) and beyond from Andrew Howroyd, Nov 03 2018

Status

approved