A175378 - OEIS

%I #15 Sep 08 2022 08:45:51

%S 0,0,0,0,1,3,5,8,14,26,45,75,125,212,358,598,993,1651,2745,4552,7526,

%T 12426,20501,33787,55605,91404,150118,246350,403929,661763,1083393,

%U 1772512,2898182,4735938,7734765,12626059,20600733,33597188,54769606

%N G.f. x^4*(2*x^2-1)/( (x^2-1)*(x^2+x-1)*(2*x^3-2*x^2+2*x-1) ).

%H Vincenzo Librandi, <a href="/A175378/b175378.txt">Table of n, a(n) for n = 0..1000</a>

%H F. V. Weinstein, <a href="http://arxiv.org/abs/math.NT/0307150">Notes on Fibonacci Partitions</a>, arXiv:math/0307150, variable h(n).

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3, -2, -1, 3, -4, 0, 2).

%F a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +3*a(n-4) -4*a(n-5) +2*a(n-7).

%t LinearRecurrence[{3,-2,-1,3,-4,0,2},{0,0,0,0,1,3,5},40] (* _Harvey P. Dale_, Mar 07 2012 *)

%t CoefficientList[Series[x^4*(2*x^2 - 1)/((x^2 - 1)*(x^2 + x - 1)*(2*x^3 - 2*x^2 + 2*x - 1)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 20 2012 *)

%o (Magma) I:=[0, 0, 0, 0, 1, 3, 5]; [n le 7 select I[n] else 3*Self(n-1) - 2*Self(n-2) - Self(n-3) + 3*Self(n-4) - 4*Self(n-5) + 2*Self(n-7): n in [1..40]]; // _Vincenzo Librandi_, Dec 20 2012

%Y Cf. A007896, A007897, A007898.

%K nonn,easy

%O 0,6

%A _R. J. Mathar_, Apr 24 2010