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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. 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: A293078 A005683 A173404 * A213710 A288382 A052968 Adjacent sequences:  A325470 A325471 A325472 * A325474 A325475 A325476 KEYWORD nonn,easy AUTHOR Brian Hopkins, Sep 06 2019 STATUS approved

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Last modified December 5 17:42 EST 2019. Contains 329768 sequences. (Running on oeis4.)