%I #9 Feb 14 2019 12:22:42
%S 1,2,4,6,9,14,23,40,73,138,267,524,1037,2062,4111,8208,16401,32786,
%T 65555,131092,262165,524310,1048599,2097176,4194329,8388634,16777243,
%U 33554460,67108893,134217758,268435487,536870944,1073741857,2147483682,4294967331,8589934628
%N a(n) = [x^n] (-x^4 + 2*x^3 - x^2 + 2*x - 1)/((x - 1)^2*(2*x - 1)).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,2).
%F a(n) = Sum_{k=0..n} binomial(n - 2, k - 1) + 1 if n >= 2.
%F a(n) = ((2 - 2*n)*a(n-2) - (5 - 3*n)*a(n-1))/(n - 2) for n >= 4.
%F a(n+1) - (n + 1) = A094373(n) for n >= 0.
%F a(n+1) - a(n) = 2^n + 1 for n >= 2.
%F a(n) = A270841(n) = 2^(n-2)+n+1 for n>=2. - _R. J. Mathar_, Feb 14 2019
%p a := proc(n) option remember; if n < 4 then return [1, 2, 4, 6][n + 1] fi;
%p ((2 - 2*n)*a(n-2) - (5 - 3*n)*a(n-1))/(n - 2) end: seq(a(n), n=0..35);
%t T[n_, k_] := If[n <= 1, 1, Binomial[n - 2, k - 1] + 1];
%t Table[Sum[T[n, k], {k, 0, n}], {n, 0, 35}]
%Y Cf. A000051, A094373.
%K nonn,easy
%O 0,2
%A _Peter Luschny_, Feb 12 2019
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