A132824 - OEIS

%I #21 Sep 28 2020 09:54:25

%S 1,2,2,4,10,24,54,116,242,496,1006,2028,4074,8168,16358,32740,65506,

%T 131040,262110,524252,1048538,2097112,4194262,8388564,16777170,

%U 33554384,67108814,134217676,268435402,536870856,1073741766,2147483588,4294967234,8589934528

%N Row sums of triangle A132823.

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

%F Binomial transform of [1, 1, -1, 3, -1, 3, -1, 3, -1, 3, ...].

%F For n>0, a(n) = 2 + 2^n - 2*n = 1 + A183155(n-1). - _R. J. Mathar_, Apr 04 2012

%F a(n) = 4*a(n-1)-5*a(n-2)+2*a(n-3) for n>3. - _Colin Barker_, Jun 06 2014

%F G.f.: -(4*x^3-x^2-2*x+1) / ((x-1)^2*(2*x-1)). - _Colin Barker_, Jun 06 2014

%F For n>1, a(n) = A132732(n-1). - _Jeppe Stig Nielsen_, Dec 29 2017

%e a(4) = 10 = sum of row 4 terms of triangle A132823: (1 + 2 + 4 + 2 + 1).

%e a(3) = 4 = (1, 3, 3, 1) dot (1, 1, -1, 3) = (1 + 3 -3 + 3).

%p A132824:=n->`if`(n=0, 1, 2+2^n-2*n); seq(A132824(n), n=0..30); # _Wesley Ivan Hurt_, Jun 06 2014

%t a[0] = 1; a[n_] := 2 + 2^n - 2*n; Table[a[n], {n, 0, 30}] (* _Wesley Ivan Hurt_, Jun 06 2014 *)

%Y Cf. A132823, A183155. Essentially the same as A132732.

%K nonn,easy

%O 0,2

%A _Gary W. Adamson_, Sep 02 2007