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%I #8 May 01 2019 09:10:45
%S 0,1,3,11,43,187,859,4059,19419,93403,450267,2172635,10487515,
%T 50632411,244463323,1180350171,5699188443,27518023387,132868585179,
%U 641545909979,3097656932059,14956809271003,72217860617947,348698671167195
%N Expansion of x*(-1+4*x)/((x-1)*(2*x-1)*(4*x^2+4*x-1)).
%H Colin Barker, <a href="/A110052/b110052.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (7,-10,-4,8).
%F From _Colin Barker_, May 01 2019: (Start)
%F a(n) = (-3/7 + 2^(-1+n) - ((-4+sqrt(2))*(2*(1+sqrt(2)))^n + (2-2*sqrt(2))^n*(4+sqrt(2))) / (28*sqrt(2))).
%F a(n) = 7*a(n-1) - 10*a(n-2) - 4*a(n-3) + 8*a(n-4) for n>3.
%F (End)
%p seriestolist(series(x*(-1+4*x)/((x-1)*(2*x-1)*(4*x^2+4*x-1)), x=0,25)); -or- Floretion Algebra Multiplication Program, FAMP Code: 2basekrokseq:[A*B] with A = + 'i - .5'j + .5'k - .5j' + .5k' - 'ii' - .5'ij' - .5'ik' - .5'ji' - .5'ki' and B = - .5'i + .5'j + 'k - .5i' + .5j' - 'kk' - .5'ik' - .5'jk' - .5'ki' - .5'kj'; RokType: Y[15] = Y[15] + 1/2
%o (PARI) concat(0, Vec(x*(1 - 4*x) / ((1 - x)*(1 - 2*x)*(1 - 4*x - 4*x^2)) + O(x^30))) \\ _Colin Barker_, May 01 2019
%Y Cf. A110050, A110051, A110053, A110054.
%K easy,nonn
%O 0,3
%A _Creighton Dement_, Jul 10 2005
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