

A069905


Number of partitions of n into 3 positive parts.


13



0, 0, 0, 1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16, 19, 21, 24, 27, 30, 33, 37, 40, 44, 48, 52, 56, 61, 65, 70, 75, 80, 85, 91, 96, 102, 108, 114, 120, 127, 133, 140, 147, 154, 161, 169, 176, 184, 192, 200, 208, 217, 225, 234, 243, 252, 261, 271, 280, 290, 300, 310, 320, 331, 341
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OFFSET

0,6


COMMENTS

Number of binary bracelets of n beads, 3 of them 0. For n>=3 a(n3) is the number of binary bracelets of n beads, 3 of them 0, with 00 prohibited. [Washington Bomfim, Aug 27 2008]
Also number of partitions of n3 into parts 1, 2, and 3. [Joerg Arndt, Sep 05 2013]
a(n) = a(n1) + A008615(n1) for n > 0.  Reinhard Zumkeller, Apr 28 2014


REFERENCES

D. E. Knuth, The Art of Computer Programming, vol. 4A, Combinatorial Algorithms, Section 7.2.1.4, p. 410.
D. E. Knuth, The Art of Computer Programming, vol. 4,fascicle 3, Generating All Combinations and Partitions, Section 7.2.1.4., p. 56, exercise 31.


LINKS

Washington Bomfim, Table of n, a(n) for n = 0..10000
Index to sequences with linear recurrences with constant coefficients, signature (1,1,0,1,1,1).


FORMULA

G.f.: x^3/((1x)*(1x^2)*(1x^3)).
a(n) = round(n^2/12).
a(n) = floor((n^2+6)/12).  Washington Bomfim, Jul 03 2012
a(n) = a(n).  Michael Somos, Sep 04 2013


EXAMPLE

x^3 + x^4 + 2*x^5 + 3*x^6 + 4*x^7 + 5*x^8 + 7*x^9 + 8*x^10 + 10*x^11 + ...


MAPLE

A069905 := n>round(n^2/12);


MATHEMATICA

a[ n_] := Round[ n^2 / 12] (* Michael Somos, Sep 04 2013 *)


PROG

(PARI) a(n) = floor((n^2+6)/12); /* Washington Bomfim, Jul 03 2012 */
(Haskell)
a069905 n = a069905_list !! n
a069905_list = scanl (+) 0 a008615_list
 Reinhard Zumkeller, Apr 28 2014


CROSSREFS

Another version of A001399, which is the main entry for this sequence.
Sequence in context: A034092 A211540 A001399 * A008761 A008760 A008759
Adjacent sequences: A069902 A069903 A069904 * A069906 A069907 A069908


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, May 04 2002


STATUS

approved



