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A174988 Expansion of -x*(x-1)*(3*x+1) / (9*x^4-8*x^2+1). 0

%I

%S 0,1,2,5,16,31,110,203,736,1345,4898,8933,32560,59359,216398,394475,

%T 1438144,2621569,9557570,17422277,63517264,115784095,422119982,

%U 769472267,2805304480,5113721281,18643356002,33984519845,123899107696

%N Expansion of -x*(x-1)*(3*x+1) / (9*x^4-8*x^2+1).

%C Old name was: a(n)=2^Floor[n/2]*((1 + Sqrt[7])^n - (1 - Sqrt[7])^n)/(2^n*Sqrt[7]).

%D Murat Sahin and Elif Tan, Conditional (strong) divisibility sequences, Fib. Q., 56 (No. 1, 2018), 18-31.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,8,0,-9).

%F a(n) = 8*a(n-2)-9*a(n-4). G.f.: -x*(x-1)*(3*x+1)/(9*x^4-8*x^2+1). [_Colin Barker_, Jan 05 2013]

%t f[n_] = 2^Floor[n/2]*((1 + Sqrt[7])^n - (1 - Sqrt[7])^n)/(2^n*Sqrt[7]);

%t Table[FullSimplify[ExpandAll[f[n]]], {n, 0, 30}]

%t LinearRecurrence[{0,8,0,-9},{0,1,2,5},30] (* _Harvey P. Dale_, Aug 21 2014 *)

%o (PARI) concat(0,Vec((1-x)*(3*x+1)/(9*x^4-8*x^2+1)+O(x^99))) \\ _Charles R Greathouse IV_, May 15 2013

%K nonn,easy

%O 0,3

%A _Roger L. Bagula_, Apr 03 2010

%E New name from _Colin Barker_, Jan 05 2013

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Last modified June 19 23:27 EDT 2021. Contains 345154 sequences. (Running on oeis4.)