A179744 - OEIS

%I #14 Jul 14 2015 01:09:26

%S 1,2,4,9,20,43,90,185,376,759,1526,3061,6132,12275,24562,49137,98288,

%T 196591,393198,786413,1572844,3145707,6291434,12582889,25165800,

%U 50331623,100663270,201326565,402653156,805306339,1610612706,3221225441

%N a(0) = 1, a(n) = 3*2^(n-1) - n for n>0.

%C Equals row sums of triangle A179743.

%C Essentially the same as A133095 and A123720. - _R. J. Mathar_, Jul 26 2010

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,2).

%F a(0) = 1, a(1) = 2; a(n) = 2*a(n-1) + (n-2) for n>1.

%F G.f. 1-x*(2-4*x+3*x^2) / ( (2*x-1)*(x-1)^2 ). - _R. J. Mathar_, May 03 2013

%e a(5) = 43 = 2*a(4) + 3 = 2*20 + 3

%e a(5) = 43 = sum of row 5 terms, triangle A179743: (1 + 5 + 8 + 12 + 16 + 1).

%t a[0] = 1; a[1] = 2; a[n_] := a[n] = 2 a[n - 1] + (n - 2); Array[a, 35, 0] (* _Robert G. Wilson v_, Aug 03 2010 *)

%o (PARI) a(n)=3*2^n\2-n \\ _Charles R Greathouse IV_, May 03 2013

%Y Cf. A179743.

%K nonn,easy

%O 0,2

%A _Gary W. Adamson_, Jul 25 2010

%E More terms from _Robert G. Wilson v_, Aug 03 2010