A171473 - OEIS

%I #20 Sep 27 2023 16:43:03

%S 35,135,527,2079,8255,32895,131327,524799,2098175,8390655,33558527,

%T 134225919,536887295,2147516415,8590000127,34359869439,137439215615,

%U 549756338175,2199024304127,8796095119359,35184376283135

%N a(n) = 6*a(n-1) - 8*a(n-2)-3 for n > 1; a(0) = 35, a(1) = 135.

%C Related to Reverse and Add trajectory of 22 in base 2: A061561(4*n+3) = 3*a(n).

%H Vincenzo Librandi, <a href="/A171473/b171473.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-14,8).

%F a(n) = 32*4^n + 4*2^n - 1.

%F G.f.: (35-110*x+72*x^2)/((1-x)*(1-2*x)*(1-4*x)).

%F a(n) = A092431(n+3).

%F a(n+1) - a(n) = A049775(n+5).

%F E.g.f.: exp(x)*(32*exp(3*x) + 4*exp(x) - 1). - _Stefano Spezia_, Sep 27 2023

%o (PARI) {m=20; v=concat([35, 135], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-8*v[n-2]-3); v}

%o (Magma) [32*4^n+4*2^n-1: n in [0..30]]; // _Vincenzo Librandi_, Jul 18 2011

%Y Cf. A061561, A092431, A049775, A171470, A171471, A171472.

%K nonn,easy

%O 0,1

%A _Klaus Brockhaus_, Dec 09 2009