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A109610 Expansion of (1+3*x^4-2*x^7+x^10-x^12)/((x+1)*(x^2+1)*(x^2+x+1)*(x^2-x+1)*(x^4-x^2+1)*(x-1)^2). 0

%I #8 Aug 19 2015 08:42:47

%S 1,1,1,1,4,4,4,2,2,2,3,3,3,3,3,3,6,6,6,4,4,4,5,5,5,5,5,5,8,8,8,6,6,6,

%T 7,7,7,7,7,7,10,10,10,8,8,8,9,9,9,9,9,9,12,12,12,10,10,10,11,11,11,11,

%U 11,11,14,14,14,12,12,12,13,13,13,13,13,13,16,16,16,14,14,14,15,15,15,15

%N Expansion of (1+3*x^4-2*x^7+x^10-x^12)/((x+1)*(x^2+1)*(x^2+x+1)*(x^2-x+1)*(x^4-x^2+1)*(x-1)^2).

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

%F a(0)=1, a(1)=1, a(2)=1, a(3)=1, a(4)=4, a(5)=4, a(6)=4, a(7)=2, a(8)=2, a(9)=2, a(10)=3, a(11)=3, a(12)=3, a(n)=a(n-1)+a(n-12)-a(n-13). - _Harvey P. Dale_, Aug 19 2015

%p seriestolist(series((1+3*x^4-2*x^7+x^10-x^12)/((x+1)*(x^2+1)*(x^2+x+1)*(x^2-x+1)*(x^4-x^2+1)*(x-1)^2), x=0,150)); -or- Floretion Algebra Multiplication Program, FAMP Code: 4baseisumseq[ .25'i + .25i' + .25'ii' + .25'jj' + .25'kk' + .25'jk' + .25'kj' + .25e]. Sumtype is set to: sum[Y[15]] = sum[ * ]

%t CoefficientList[Series[(1+3x^4-2x^7+x^10-x^12)/((x+1)(x^2+1)(x^2+x+1)(x^2-x+1)(x^4-x^2+1)(x-1)^2),{x,0,100}],x] (* or *) LinearRecurrence[ {1,0,0,0,0,0,0,0,0,0,0,1,-1},{1,1,1,1,4,4,4,2,2,2,3,3,3},100] (* _Harvey P. Dale_, Aug 19 2015 *)

%K nonn

%O 0,5

%A _Creighton Dement_, Jul 31 2005

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