A155629 - OEIS

%I #26 Jul 30 2024 06:00:43

%S 1,5,49,449,3841,31745,258049,2080769,16711681,133955585,1072693249,

%T 8585740289,68702699521,549688705025,4397778075649,35183298347009,

%U 281470681743361,2251782633816065,18014329790005249,144114913197948929,1152920405095219201,9223367638808264705

%N a(n) = 8^n - 4^n + 1.

%H Paolo Xausa, <a href="/A155629/b155629.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (13,-44,32).

%F G.f.: 1/(1-8*x)-1/(1-4*x)+1/(1-x).

%F E.g.f.: exp(8*x)-exp(4*x)+exp(x).

%F a(n) = 12*a(n-1)-32*a(n-2)+21 with a(0) = 1, a(1) = 5. - _Vincenzo Librandi_, Jul 21 2010

%t Table[8^n - 4^n + 1, {n, 0, 25}] (* _Paolo Xausa_, Jul 30 2024 *)

%o (PARI) a(n)=8^n-4^n+1 \\ _Charles R Greathouse IV_, Sep 24 2015

%Y Cf. A155596, A155597, A155598, A155599, A155600, A155601, A155622, A155623, A155624, A155625, A155626, A155627, A155628.

%K nonn,easy

%O 0,2

%A _Mohammad K. Azarian_, Jan 30 2009