A171472 - OEIS

%I #32 Sep 27 2023 16:41:43

%S 7,30,124,504,2032,8160,32704,130944,524032,2096640,8387584,33552384,

%T 134213632,536862720,2147467264,8589901824,34359672832,137438822400,

%U 549755551744,2199022731264,8796091973632,35184369991680

%N a(n) = 6*a(n-1) - 8*a(n-2) for n > 1; a(0) = 7, a(1) = 30.

%C Related to Reverse and Add trajectory of 22 in base 2: A061561(4*n+2) = 12*a(n).

%C Third binomial transform of A010729.

%C a(n) in base 2 is n+3 1s followed by n 0s. - _Hussam al-Homsi_, Oct 12 2021

%H Vincenzo Librandi, <a href="/A171472/b171472.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-8).

%F a(n) = 8*4^n-2^n.

%F G.f.: (7-12*x)/((1-2*x)*(1-4*x)).

%F a(n) = A171499(n+1)/2. - _Hussam al-Homsi_, Jun 06 2021

%F E.g.f.: exp(2*x)*(8*exp(2*x) - 1). - _Stefano Spezia_, Sep 27 2023

%t LinearRecurrence[{6,-8},{7,30},30] (* _Harvey P. Dale_, Sep 01 2016 *)

%o (PARI) {m=22; v=concat([7, 30], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-8*v[n-2]); v}

%o (Magma) [8*4^n-2^n: n in [0..30]]; // _Vincenzo Librandi_, May 31 2011

%Y Cf. A061561, A010729 (repeat 7, 9), A171470, A171471, A171473, A171499.

%K nonn,easy

%O 0,1

%A _Klaus Brockhaus_, Dec 09 2009