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A075112 a(n)=Sum((-1)^(i+Floor(n/2))S(2i+e),(i=0,..,Floor(n/2))), where S(n) are generalized Tetranacci numbers (A073817) and e=(1/2)(1-(-1)^n). 0

%I

%S 4,1,-1,6,16,20,35,79,156,288,552,1077,2079,3994,7696,14848,28623,

%T 55159,106320,204952,395060,761489,1467815,2829318,5453688,10512308,

%U 20263123,39058439,75287564,145121432,279730552,539197989,1039337543,2003387514,3861653592,7443576640,14347955295

%N a(n)=Sum((-1)^(i+Floor(n/2))S(2i+e),(i=0,..,Floor(n/2))), where S(n) are generalized Tetranacci numbers (A073817) and e=(1/2)(1-(-1)^n).

%C a(n) is the convolution of S(n) with the sequence (1,0,-1,0,1,0,-1,0,....) A056594.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 2, 2, 1, 1).

%F a(n)=a(n-1)+2a(n-3)+2a(n-4)+a(n-5)+a(n-6), a(0)=4, a(1)=1, a(2)=-1, a(3)=6, a(4)=16, a(5)=20. G.f.: (4 - 3*x - 2*x^2 - x^3)/(1 - x - 2*x^3 - 2*x^4 - x^5 - x^6).

%t CoefficientList[Series[(4 - 3*x - 2*x^2 - x^3)/(1 - x - 2*x^3 - 2*x^4 - x^5 - x^6), {x, 0, 40}], x]

%t LinearRecurrence[{1,0,2,2,1,1},{4,1,-1,6,16,20},40] (* _Harvey P. Dale_, Mar 09 2013 *)

%Y Cf. A073817, A056594, A074662, A074677, A074678, A075111.

%K easy,sign

%O 0,1

%A Mario Catalani (mario.catalani(AT)unito.it), Sep 01 2002

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Last modified September 23 03:04 EDT 2020. Contains 337291 sequences. (Running on oeis4.)