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A006501 Expansion of (1+x^2) / ( (1-x)^2 * (1-x^3)^2 ).
(Formerly M1091)
4
1, 2, 4, 8, 12, 18, 27, 36, 48, 64, 80, 100, 125, 150, 180, 216, 252, 294, 343, 392, 448, 512, 576, 648, 729, 810, 900, 1000, 1100, 1210, 1331, 1452, 1584, 1728, 1872, 2028, 2197, 2366, 2548, 2744, 2940, 3150, 3375, 3600, 3840, 4096, 4352, 4624, 4913, 5202 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n+3) = maximal product of three numbers with sum n: a(n) = max(r*s*t), n = r+s+t. - Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jul 10 2003

It appears that k is a term of the sequence if and only if k is a positive integer such that floor(v) * ceiling(v) * round(v) = k, where v = k^(1/3). - John W. Layman, Mar 21 2012

The sequence floor(n/3)*floor((n+1)/3)*floor((n+2)/3) is essentially the same: 0, 0, 0, 1, 2, 4, 8, 12, 18, 27, 36, 48, 64, 80, 100, 125, 150, 180, 216, 252, ... - N. J. A. Sloane, Dec 27 2013

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

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

G. E. Bergum and V. E. Hoggatt, Jr., A combinatorial problem involving recursive sequences and tridiagonal matrices, Fib. Quart., 16 (1978), 113-118.

Dhruv Mubayi, Counting substructures II: Hypergraphs, Combinatorica 33 (2013), no. 5, 591--612. MR3132928

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

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

FORMULA

a(n) = [(n+3)/3] * [(n+4)/3] * [(n+5)/3]. - Reinhard Zumkeller, May 18 2004

a(n-3) = sum(k=0..n, [k/3][(k+1)/3]). - Mitch Harris, Dec 02 2004

Conjecture: a(n) = A144677(n)+A144677(n-2). - R. J. Mathar, Mar 15 2011

MAPLE

A006501:=(1+z**2)/(z**2+z+1)**2/(z-1)**4; # Simon Plouffe in his 1992 dissertation

MATHEMATICA

CoefficientList[Series[(1+x^2)/(1-x)^2 /(1-x^3)^2, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 16 2012 *)

CROSSREFS

Cf. A002620, A210433

Sequence in context: A284122 A212585 A085891 * A224814 A224810 A074633

Adjacent sequences:  A006498 A006499 A006500 * A006502 A006503 A006504

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Reinhard Zumkeller, May 18 2004

STATUS

approved

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Last modified November 23 20:23 EST 2017. Contains 295141 sequences.