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 A125301 a(3n) = n, a(3n+1) = (n+2)*a(3n), a(3n+2) = (n+2)*a(3n+1). 1
 0, 0, 0, 1, 3, 9, 2, 8, 32, 3, 15, 75, 4, 24, 144, 5, 35, 245, 6, 48, 384, 7, 63, 567, 8, 80, 800, 9, 99, 1089, 10, 120, 1440, 11, 143, 1859, 12, 168, 2352, 13, 195, 2925, 14, 224, 3584, 15, 255, 4335, 16, 288, 5184, 17, 323, 6137, 18, 360, 7200, 19, 399, 8379, 20 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS From a competency test. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (0,0,4,0,0,-6,0,0,4,0,0,-1). FORMULA From Colin Barker, Jan 24 2017: (Start) a(n) = 4*a(n-3) - 6*a(n-6) + 4*a(n-9) - a(n-12) for n>11. G.f.: x^3*(1 + 3*x + 9*x^2 - 2*x^3 - 4*x^4 - 4*x^5 + x^6 + x^7 + x^8) / ((1 - x)^4*(1 + x + x^2)^4). (End) MAPLE a:=proc(n): if n mod 3=0 then n/3 elif n mod 3 = 1 then (n+5)*a(n-1)/3 else (n+4)*a(n-1)/3 fi end: seq(a(n), n=0..75); # Emeric Deutsch, Jan 01 2007 MATHEMATICA LinearRecurrence[{0, 0, 4, 0, 0, -6, 0, 0, 4, 0, 0, -1}, {0, 0, 0, 1, 3, 9, 2, 8, 32, 3, 15, 75}, 70] (* Harvey P. Dale, Jul 31 2018 *) PROG (PARI) concat(vector(3), Vec(x^3*(1 + 3*x + 9*x^2 - 2*x^3 - 4*x^4 - 4*x^5 + x^6 + x^7 + x^8) / ((1 - x)^4*(1 + x + x^2)^4) + O(x^100))) \\ Colin Barker, Jan 24 2017 CROSSREFS Sequence in context: A348371 A354129 A060956 * A347214 A263559 A262343 Adjacent sequences: A125298 A125299 A125300 * A125302 A125303 A125304 KEYWORD nonn,easy AUTHOR Trent Stratton (trent.stratton(AT)gov.bc.ca), Dec 08 2006 EXTENSIONS Solution from N. J. A. Sloane, Dec 08 2006 More terms from Emeric Deutsch, Jan 01 2007 STATUS approved

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Last modified July 25 09:25 EDT 2024. Contains 374587 sequences. (Running on oeis4.)