%I #19 Mar 10 2024 03:08:20
%S 1,2,4,8,16,32,62,124,248,494,988,1976,3952,7904,15808,31616,63232,
%T 126464,252926,505852,1011704,2023406,4046812,8093624,16187248,
%U 32374496,64748992,129497984,258995968,517991936,1035983870,2071967740
%N Expansion of (-1+x^3+x^6+x^9)/((1-x)*(2*x-1)*(x^2+1)*(x^2+x+1)*(x^4-x^2+1)).
%C Initial terms factored: [1,2,(2)^2,(2)^3,(2)^4,(2)^5,(2) (31),(2)^2 (31),(2)^3 (31),(2) (13) (19),(2)^2 (13) (19),(2)^3 (13) (19),(2)^4 (13) (19),(2)^5 (13) (19),(2)^6 (13) (19),(2)^7 (13) (19),(2)^8 (13) (19),(2)^9 (13) (19),(2) (17) (43) (173),(2)^2 (17) (43) (173),(2)^3 (17) (43) (173),(2) (7)^2 (11) (1877),(2)^2 (7)^2 (11) (1877),(2)^3 (7)^2 (11) (1877),(2)^4 (7)^2 (11) (1877),(2)^5 (7)^2 (11) (1877),(2)^6 (7)^2 (11) (1877),(2)^7 (7)^2 (11) (1877),(2)^8 (7)^2 (11) (1877),(2)^9 (7)^2 (11) (1877)]
%C Floretion Algebra Multiplication Program, FAMP Code: 2jbaseksumseq[.5'i + .5i' + .5'ii' + .5'jj' + .5'kk' + .5e], sumtype: sum[(Y[0], Y[1], Y[2]),mod(3)
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,1,-2,0,-1,2,0,1,-2).
%F a(0)=1, a(1)=2, a(2)=4, a(3)=8, a(4)=16, a(5)=32, a(6)=62, a(7)=124, a(8)=248, a(9)=494, a(n) = 2*a(n-1)+a(n-3)-2*a(n-4)-a(n-6)+2*a(n-7)+ a(n-9)- 2*a(n-10). [_Harvey P. Dale_, May 04 2012]
%t CoefficientList[Series[(-1+x^3+x^6+x^9)/((1-x)(2x-1)(x^2+1)*(x^2+x+1)(x^4-x^2+1)),{x,0,40}],x] (* or *) LinearRecurrence[{2,0,1,-2,0,-1,2,0,1,-2},{1,2,4,8,16,32,62,124,248,494},40] (* _Harvey P. Dale_, May 04 2012 *)
%o (PARI) Vec((-1+x^3+x^6+x^9)/((1-x)*(2*x-1)*(x^2+1)*(x^2+x+1)*(x^4-x^2+1))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 27 2012
%Y Cf. A111662.
%K nonn,easy
%O 0,2
%A _Creighton Dement_, Aug 14 2005