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A109785 Expansion of (1+x+x^2+x^7+x^8-2*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). 1

%I

%S 1,2,3,3,3,3,3,4,5,5,3,3,3,4,5,5,5,5,5,6,7,7,5,5,5,6,7,7,7,7,7,8,9,9,

%T 7,7,7,8,9,9,9,9,9,10,11,11,9,9,9,10,11,11,11,11,11,12,13,13,11,11,11,

%U 12,13,13,13,13,13,14,15,15,13,13,13,14,15,15,15,15,15,16,17,17,15,15,15

%N Expansion of (1+x+x^2+x^7+x^8-2*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 Colin Barker, <a href="/A109785/b109785.txt">Table of n, a(n) for n = 0..1000</a>

%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(n) = a(n-1) + a(n-12) - a(n-13) for n>12. - _Colin Barker_, May 15 2019

%t CoefficientList[Series[(1+x+x^2+x^7+x^8-2x^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,0,90}],x] (* _Harvey P. Dale_, Oct 21 2011 *)

%o Floretion Algebra Multiplication Program, FAMP Code: 1jbasesumseq[(- .5'j + .5'k - .5j' + .5k' - 'ii' - .5'ij' - .5'ik' - .5'ji' - .5'ki')*(- .5'i + .5'j - .5i' + .5j' - 'kk' - .5'ik' - .5'jk' - .5'ki' - .5'kj')], sumtype: (default, ver. f, ves)

%o (PARI) Vec((1 + x + x^2 + x^7 + x^8 - 2*x^10 - x^12) / ((1 - x)^2*(1 + x)*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)*(1 - x^2 + x^4)) + O(x^100)) \\ _Colin Barker_, May 15 2019

%K nonn,easy

%O 0,2

%A _Creighton Dement_, Aug 14 2005

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Last modified October 19 15:34 EDT 2021. Contains 348091 sequences. (Running on oeis4.)