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, 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

Offset

0,3

Links

Table of n, a(n) for n=0..37.

L. Moser and E. L. Whitney, Weighted compositions, Canad. Math. Bull. 4 (1961), 39-43.

Index entries for linear recurrences with constant coefficients, signature (3,-2,0,-1,1)

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

Cf. A001590, A062544.

Sequence in context: A005683 A329698 A173404 * A213710 A288382 A052968

Adjacent sequences: A325470 A325471 A325472 * A325474 A325475 A325476

Keyword

nonn,easy

Author

Brian Hopkins, Sep 06 2019

Status

approved