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a(n) = 2*A016777(n) + A016777(n-1) - (n+1).
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%I #19 Mar 23 2022 07:39:46

%S 1,7,15,23,31,39,47,55,63,71,79,87,95,103,111,119,127,135,143,151,159,

%T 167,175,183,191,199,207,215,223,231,239,247,255,263,271,279,287,295,

%U 303,311,319,327,335,343,351,359,367,375,383,391,399,407,415

%N a(n) = 2*A016777(n) + A016777(n-1) - (n+1).

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F Equals "1" followed by A004771.

%F Binomial transform of [1, 6, 2, -2, 2, -2, 2, ...].

%F G.f.: (2*x^2+5*x+1)/(x-1)^2. - _Harvey P. Dale_, Sep 13 2011

%e a(3) = 23 = 2*A016777(3) + A016777(2) - 4 = 2*10 + 7 - 4.

%e a(3) = 23 = (1, 3, 3, 1) dot (1, 6, 2, -2) = (1, 18, 6, -2).

%t CoefficientList[Series[(2 x^2+5 x+1)/(x-1)^2,{x,0,60}],x] (* _Harvey P. Dale_, Sep 13 2011 *)

%Y Cf. A004771, A016777.

%K nonn,easy

%O 0,2

%A _Gary W. Adamson_, Sep 20 2007

%E More terms and corrected definition from _R. J. Mathar_, Jun 08 2008