A008822 Expansion of (1 + 2*x^2 + x^3)/((1 - x)^2*(1 - x^3)).

1, 2, 5, 10, 15, 22, 31, 40, 51, 64, 77, 92, 109, 126, 145, 166, 187, 210, 235, 260, 287, 316, 345, 376, 409, 442, 477, 514, 551, 590, 631, 672, 715, 760, 805, 852, 901, 950, 1001, 1054, 1107, 1162, 1219, 1276, 1335, 1396, 1457, 1520, 1585, 1650, 1717, 1786, 1855, 1926, 1999, 2072

Offset

0,2

Comments

Corresponds to the best known lower bound for the tie problem. - Jörg Zurkirchen, Oct 15 2008

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

R. Chapman et al., 2-modular lattices from ternary codes, J. Th. des Nombres de Bordeaux, 14 (2002), 73-85.

Index entries for Molien series

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

Formula

a(n) = ceiling((n+1)*(2*n+1)/3). - Jörg Zurkirchen, Oct 15 2008

a(n) = (n+1)^2 - floor((n+1)*(n+2)/3). - Bruno Berselli, Mar 02 2017

Maple

seq(ceil((n+1)*(2*n+1)/3), n=0..60); # G. C. Greubel, Sep 13 2019

Mathematica

CoefficientList[Series[(1+2x^2+x^3)/((1-x)^2(1-x^3)), {x, 0, 60}], x] (* or *) LinearRecurrence[{2, -1, 1, -2, 1}, {1, 2, 5, 10, 15}, 60] (* Vincenzo Librandi, Mar 31 2017 *)

Prog

(PARI) Vec((1+2*x^2+x^3)/((1-x)^2*(1-x^3)) + O(x^80)) \\ Michel Marcus, Oct 28 2015
(Magma) [Ceiling((n+1)*(2*n+1)/3): n in [0..60]]; // Vincenzo Librandi, Mar 31 2017
(Sage) [ceil((n+1)*(2*n+1)/3) for n in (0..60)] # G. C. Greubel, Sep 13 2019
(GAP) a:=[1, 2, 5, 10, 15];; for n in [6..60] do a[n]:=2*a[n-1]-a[n-2] +a[n-3]-2*a[n-4]+a[n-5]; od; a; # G. C. Greubel, Sep 13 2019

Crossrefs

Expansions of the form (1 +2*x^(m+1) +x^(2*m+1))/((1-x)^2*(1-x^(2*m+1))): this sequence (m=1), A008823 (m=2), A008824 (m=3), A008825 (m=4).

Sequence in context: A125622 A080551 A179207 * A267454 A013927 A163059

Adjacent sequences: A008819 A008820 A008821 * A008823 A008824 A008825

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved