A134067 - OEIS

%I #31 May 08 2023 09:35:19

%S 1,6,14,30,62,126,254,510,1022,2046,4094,8190,16382,32766,65534,

%T 131070,262142,524286,1048574,2097150,4194302,8388606,16777214,

%U 33554430,67108862,134217726,268435454,536870910,1073741822,2147483646,4294967294,8589934590,17179869182

%N Row sums of triangle A134066.

%C Essentially the same as A095121. - _R. J. Mathar_, Mar 28 2012

%H Vincenzo Librandi, <a href="/A134067/b134067.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).

%F Binomial transform of (1, 5, 3, 5, 3, 5, ...).

%F From _Colin Barker_, Mar 13 2014: (Start)

%F a(n) = 2^(2+n) - 2 for n > 0.

%F a(n) = 3*a(n-1) - 2*a(n-2) for n > 0.

%F G.f.: -(2*x^2-3*x-1) / ((x-1)*(2*x-1)). (End)

%F E.g.f.: 2*exp(x)*(2*exp(x) - 1) - 1. - _Stefano Spezia_, May 07 2023

%e a(3) = 30 = sum of row 3 terms of triangle A134066: (2 + 12 + 12 + 4).

%e a(3) = 30 = (1, 3, 3, 1) dot (1, 5, 3, 5) = (1 + 15 + 9 + 5).

%t Join[{1}, LinearRecurrence[{3, -2}, {6, 14}, 50]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 23 2012 *)

%o (PARI) Vec(-(2*x^2-3*x-1)/((x-1)*(2*x-1)) + O(x^100)) \\ _Colin Barker_, Mar 13 2014

%Y Cf. A095121, A134066.

%K nonn,easy

%O 0,2

%A _Gary W. Adamson_, Oct 06 2007