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a(n) = 15*2^(n+1) - (5*n^2+22*n+30).
1

%I #15 Sep 19 2017 04:04:38

%S 0,3,26,99,282,695,1578,3411,7154,14727,29970,60563,121866,244599,

%T 490202,981555,1964418,3930311,7862274,15726387,31454810,62911863,

%U 125826186,251655059,503313042,1006629255,2013261938,4026527571,8053059114,16106122487,32212249530

%N a(n) = 15*2^(n+1) - (5*n^2+22*n+30).

%H B. Berselli, <a href="/A169832/b169832.txt">Table of n, a(n) for n = 0..1000</a> [From _Bruno Berselli_, Jun 03 2010]

%H P. Nissen and J. Taylor, <a href="http://www.jstor.org/stable/2690454">Running clubs - a combinatorial investigation</a>, Math. Mag., 64 (No. 1, 1991), 39-44.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,7,-2). [From _R. J. Mathar_, Jun 04 2010]

%F From _Bruno Berselli_ and _R. J. Mathar_, Jun 03 2010: (Start)

%F G.f.: x*(3+11*x-4*x^2)/[(1-2*x)*(1-x)^3].

%F a(n) - 5*a(n-1) + 9*a(n-2) - 7*a(n-3) + 2*a(n-4) = 0, with n>3. (End)

%t LinearRecurrence[{5,-9,7,-2},{0,3,26,99},40] (* _Harvey P. Dale_, Sep 24 2014 *)

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Jun 01 2010