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A092353 Expansion of (1+x^3)/((1-x)^2*(1-x^3)^2). 3
1, 2, 3, 7, 11, 15, 24, 33, 42, 58, 74, 90, 115, 140, 165, 201, 237, 273, 322, 371, 420, 484, 548, 612, 693, 774, 855, 955, 1055, 1155, 1276, 1397, 1518, 1662, 1806, 1950, 2119, 2288, 2457, 2653, 2849, 3045, 3270, 3495, 3720, 3976, 4232, 4488, 4777, 5066, 5355, 5679 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.

Index entries for linear recurrences with constant coefficients, signature (2,-1,2,-4,2,-1,2,-1).

FORMULA

G.f.: (1+x^3)/((1-x)^2*(1-x^3)^2) = (1+x^3)/((1-x)^4*(1+x+x^2)^2).

a(n) = Sum(i=1..n+3, floor(i/3)^2). - Enrique Pérez Herrero, Mar 20 2012

a(n) = (1/2)*(-4*t^3 + (2n-7)*t^2 + (4n-1)*t +2n +2), where t = floor(n/3). - Ridouane Oudra, Oct 19 2019

MAPLE

seq(add(floor(i/3)^2, i=1..n+3), n=0..60); # Ridouane Oudra, Oct 19 2019

MATHEMATICA

a[n_] := Sum[Floor[i/3]^2, {i, 1, n+3}]; Table[a[n], {n, 0, 100}] (* Enrique Pérez Herrero, Mar 20 2012 *)

PROG

(Sage)

def A092353():

    a, b, c, m = 0, 0, 0, 0

    while True:

        yield (a*(a*(2*a+9)+13)+b*(b+1)*(2*b+1)+c*(c+1)*(2*c+1)+6)//6

        m = m + 1 if m < 2 else 0

        if   m == 0: a += 1

        elif m == 1: b += 1

        elif m == 2: c += 1

a = A092353()

print([next(a) for _ in range(52)]) # Peter Luschny, May 04 2016

CROSSREFS

Cf. A005993.

Sequence in context: A188529 A174060 A285278 * A189374 A180516 A100963

Adjacent sequences:  A092350 A092351 A092352 * A092354 A092355 A092356

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Mar 20 2004

STATUS

approved

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Last modified December 2 23:22 EST 2021. Contains 349445 sequences. (Running on oeis4.)