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A325473 Number of compositions of n with no part divisible by 3 and an even number of parts congruent to 4 or 5 modulo 6. 1
1, 1, 2, 3, 5, 8, 13, 22, 38, 67, 120, 217, 395, 722, 1323, 2428, 4460, 8197, 15070, 27711, 50961, 93724, 172377, 317042, 583122, 1072519, 1972660, 3628277, 6673431, 12274342, 22576023, 41523768, 76374104, 140473865, 258371706, 475219643, 874065181, 1607656496 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
L. Moser and E. L. Whitney, Weighted compositions, Canad. Math. Bull. 4 (1961), 39-43.
FORMULA
a(n) = (A001590(n+2) + n)/2, see Moser & Whitley reference, Theorem 3.
a(n) = A062544(n-3) + n for n >= 3 (also for n = 1 and 2 with A062544(-2) = A062544(-1) = 0), Moser & Whitney.
G.f.: (x^5-x^4+x^3-x^2+2*x-1)/((x^3+x^2+x-1)*(x-1)^2). - Alois P. Heinz, Sep 06 2019
EXAMPLE
a(4) counts (1,1,1,1), (1,1,2), (1,2,1), (2,1,1), (2,2), but not (1,3) or (3,1) since they contain 3, neither (4) since that has an odd number of parts congruent to 4 or 5 mod 6.
CROSSREFS
Sequence in context: A005683 A329698 A173404 * A213710 A288382 A052968
KEYWORD
nonn,easy
AUTHOR
Brian Hopkins, Sep 06 2019
STATUS
approved

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Last modified March 28 16:34 EDT 2024. Contains 371254 sequences. (Running on oeis4.)