A084672 Expansion of g.f.: (1+x^2+2*x^4)/((1-x^3)*(1-x)^2).

1, 2, 4, 7, 12, 18, 25, 34, 44, 55, 68, 82, 97, 114, 132, 151, 172, 194, 217, 242, 268, 295, 324, 354, 385, 418, 452, 487, 524, 562, 601, 642, 684, 727, 772, 818, 865, 914, 964, 1015, 1068, 1122, 1177, 1234, 1292, 1351, 1412, 1474, 1537, 1602, 1668, 1735, 1804, 1874

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

J. Hietarinta and C.-M. Viallet, Discrete Painlevé I and singularity confinement in projective space, Chaos, Solitons and Fractals 11, 2000, p. 29.

Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1).

Formula

From G. C. Greubel, Mar 22 2023: (Start)

a(n) = (1/3)*(2*n^2 - n + 3 + 2*floor((n+2)/3) + floor((n+1)/3)).

a(n) = (1/9)*(6*n^2 + 11 - 2*A049347(n) - A049347(n-1)). (End)

Mathematica

CoefficientList[Series[(1+x^2+2x^4)/((1-x^3)(1-x)^2), {x, 0, 70}], x]  (* Harvey P. Dale, Mar 31 2011 *)

Prog

(PARI) Vec((1+x^2+2*x^4)/(1-x^3)/(1-x)^2+O(x^99)) \\ Charles R Greathouse IV, Sep 10 2014
(Magma) [(2*n^2 -n +3 +2*Floor((n+2)/3) +Floor((n+1)/3))/3: n in [0..60]]; // G. C. Greubel, Mar 22 2023
(SageMath) [(2*n^2 -n +3 +2*((n+2)//3) +((n+1)//3))/3 for n in range(61)] # G. C. Greubel, Mar 22 2023

Crossrefs

Cf. A049347.

Sequence in context: A346114 A332744 A345731 * A011910 A227590 A267529

Adjacent sequences: A084669 A084670 A084671 * A084673 A084674 A084675

Keyword

nonn,easy

Author

N. J. A. Sloane, Jul 16 2003

Status

approved