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%I #19 Mar 13 2024 19:25:58
%S 0,1,1,2,3,3,5,8,11,19,29,42,67,99,149,232,347,531,813,1226,1875,2851,
%T 4325,6600,10027,15251,23229,35306,53731,81763,124341,189224,287867,
%U 437907,666317,1013642,1542131,2346275,3569413,5430536,8261963,12569363
%N G.f. x*(x^2+1)*(x^3-x-1)/((2*x^3+x^2-1)*(x^4+1)).
%C The sequence A078028 is given by 1em[I* ]forzapseq and is from the same "batch" (i.e., corresponding to the same floretion and symmetry settings) as A107849, A107850, A107851, A107852, A107853 and (a(n)).
%C Floretion Algebra Multiplication Program, FAMP Code: 1dia[I]forzapseq[(.5i' + .5j' + .5'ki' + .5'kj')*(.5'i + .5'j + .5'ik' + .5'jk')], 1vesforzap = A000004
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,2,-1,0,1,2).
%F a(n) = A159284(n) + A014017(n+5).
%t CoefficientList[Series[x(x^2+1)(x^3-x-1)/((2x^3+x^2-1)(x^4+1)),{x,0,50}],x] (* or *) LinearRecurrence[{0,1,2,-1,0,1,2},{0,1,1,2,3,3,5},50] (* _Harvey P. Dale_, Jun 21 2022 *)
%o (PARI) a(n)=([0,1,0,0,0,0,0; 0,0,1,0,0,0,0; 0,0,0,1,0,0,0; 0,0,0,0,1,0,0; 0,0,0,0,0,1,0; 0,0,0,0,0,0,1; 2,1,0,-1,2,1,0]^n*[0;1;1;2;3;3;5])[1,1] \\ _Charles R Greathouse IV_, Oct 03 2016
%Y Cf. A107849, A107850, A107851, A107852, A107853, A078028.
%K easy,nonn
%O 0,4
%A _Creighton Dement_, May 25 2005
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