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%I #25 Mar 06 2024 15:47:33
%S 1,3,7,19,53,155,459,1371,4105,12307,36911,110723,332157,996459,
%T 2989363,8968075,26904209,80712611,242137815,726413427,2179240261,
%U 6537720763,19613162267,58839486779,176518460313,529555380915,1588666142719,4765998428131
%N Expansion of (-1+x+3*x^2-x^3)/((x+1)(3*x-1)(x-1)^2).
%C A floretion-generated sequence relating to A081250 (Numbers n such that A081249(m)/m^2 has a local minimum for m = n).
%C Binomial transform starts: 1, 4, 14, 50, 184, 696, 2688, 10528, 41600, 165248, ... - _Wesley Ivan Hurt_, Sep 12 2014
%C Floretion Algebra Multiplication Program, FAMP Code: 1famforrokseq[ - .5'j + .5'k - .5j' + .5k' - 'ii' - .5'ij' - .5'ik' - .5'ji' - .5'ki']
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-2,-4,3).
%F a(n) = (1/8) * (5*3^n + 4*(n+1) - (-1)^n). - _Ralf Stephan_, Nov 13 2010.
%F a(n+2) - 2a(n+1) + a(n) = A081250(n+1) - A081250(n).
%F a(n) = 4*a(n-1)-2*a(n-2)-4*a(n-3)+3*a(n-4). - _Wesley Ivan Hurt_, Sep 12 2014
%p A104522:=n->(5*3^n+4*(n+1)-(-1)^n)/8: seq(A104522(n), n=0..30); # _Wesley Ivan Hurt_, Sep 12 2014
%t CoefficientList[Series[(-1 + x + 3 x^2 - x^3)/((x + 1) (3*x - 1) (x - 1)^2), {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Sep 12 2014 *)
%o (Magma) [(5*3^n+4*(n+1)-(-1)^n)/8 : n in [0..30]]; // _Wesley Ivan Hurt_, Sep 12 2014
%Y Cf. A081250, A105792.
%K nonn,easy
%O 0,2
%A _Creighton Dement_, Apr 20 2005
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