A125301 a(3n) = n, a(3n+1) = (n+2)*a(3n), a(3n+2) = (n+2)*a(3n+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

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