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A145135 Expansion of x/((1 - x - x^4)*(1 - x)^6).

%I A145135 #13 Feb 17 2018 15:35:19
%S A145135 0,1,7,28,84,211,470,960,1836,3334,5806,9769,15973,25495,39869,61266,
%T A145135 92743,138587,204790,299705,434952,626669,897239,1277674,1810906,
%U A145135 2556330,3596075,5043660,7055942,9849608,13723939,19092231,26525165
%N A145135 Expansion of x/((1 - x - x^4)*(1 - x)^6).
%C A145135 The coefficients of the recursion for a(n) are given by the 7th row of A145152.
%H A145135 Vincenzo Librandi, <a href="/A145135/b145135.txt">Table of n, a(n) for n = 0..1000</a>
%F A145135 a(n) = 7a(n-1) -21a(n-2) +35a(n-3) -34a(n-4) +15a(n-5) +8a(n-6) -19a(n-7) +15a(n-8) -6a(n-9) +a(n-10).
%p A145135 col:= proc(k) local l, j, M, n; l:= `if`(k=0, [1, 0, 0, 1], [seq(coeff ( -(1-x-x^4) *(1-x)^(k-1), x, j), j=1..k+3)]); M:= Matrix(nops(l), (i,j)-> if i=j-1 then 1 elif j=1 then l[i] else 0 fi); `if`(k=0, n->(M^n)[2,3], n->(M^n)[1,2]) end: a:= col(7): seq(a(n), n=0..40);
%t A145135 CoefficientList[Series[x / ((1 - x - x^4) (1 - x)^6), {x, 0, 50}], x] (* _Vincenzo Librandi_, Jun 06 2013 *)
%o A145135 (PARI) concat(0,Vec(1/(1-x-x^4)/(1-x)^6+O(x^99))) \\ _Charles R Greathouse IV_, Sep 25 2012
%Y A145135 7th column of A145153. Cf. A145152.
%K A145135 nonn,easy
%O A145135 0,3
%A A145135 _Alois P. Heinz_, Oct 03 2008