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%I #13 Mar 13 2024 19:26:07
%S 1,4,11,29,72,175,425,1028,2483,5997,14480,34959,84401,203764,491931,
%T 1187629,2867192,6922015,16711225,40344468,97400163,235144797,
%U 567689760,1370524319,3308738401,7988001124,19284740651,46557482429,112399705512
%N Expansion of (x^2+1)*(x+1)^2 / ((x-1)*(x^2+x+1)*(x^2+2*x-1)).
%C Floretion Algebra Multiplication Program, FAMP Code: 2tessumseq[C*H] with C = - .5'j + .5'k - .5j' + .5k' - 'ii' - .5'ij' - .5'ik' - .5'ji' - .5'ki' and H = + .5'j + .5j', sumtype: (Y[sqa.Findk()], *, sum) (internal program code)
%H Colin Barker, <a href="/A109803/b109803.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,1,-2,-1).
%F a(n) = 2*a(n-1) + a(n-2) + a(n-3) - 2*a(n-4) - a(n-5) for n>4. - _Colin Barker_, May 16 2019
%F 21*a(n) = 12*( A000129(n)+4*A000129(n+1)) -4*7 +b(n) where b(n>=0) = A049347(n)+5*A049347(n-1) = 1,4,-5,1,4,-5,... periodic with period 3. - _R. J. Mathar_, Sep 11 2019
%t LinearRecurrence[{2,1,1,-2,-1},{1,4,11,29,72},40] (* _Harvey P. Dale_, May 11 2020 *)
%o (PARI) Vec((1 + x)^2*(1 + x^2) / ((1 - x)*(1 + x + x^2)*(1 - 2*x - x^2)) + O(x^35)) \\ _Colin Barker_, May 16 2019
%K easy,nonn
%O 0,2
%A _Creighton Dement_, Aug 15 2005
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