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A179608 a(n) = (7 + (-1)^n + 6*n)*2^(n-3). 3

%I #15 Jul 03 2023 11:37:26

%S 1,3,10,24,64,144,352,768,1792,3840,8704,18432,40960,86016,188416,

%T 393216,851968,1769472,3801088,7864320,16777216,34603008,73400320,

%U 150994944,318767104,654311424,1375731712,2818572288,5905580032

%N a(n) = (7 + (-1)^n + 6*n)*2^(n-3).

%C This sequence belongs to a family of sequences with g.f. (1+x)/(1 - 2*x - (k+8)*x^2 - 2*k*x^3). Among the members of this family are several red king sequences, see A179596. For the sequence given above, which is not a red king sequence, k = -4.

%C Inverse binomial transform of A119916 (without the leading 0).

%H Vincenzo Librandi, <a href="/A179608/b179608.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 (2, 4, -8).

%F G.f.: (1+x)/(1 - 4*x^2 - 2*x + 8*x^3).

%F a(n) = 2*a(n-1) + 4*a(n-2) - 8*a(n-3) with a(1)=1, a(2)=3 and a(3)=10.

%F a(n) = (7 + (-1)^n + 6*n)*2^(n-3).

%o (Magma) [(7+(-1)^n+6*n)*2^(n-3): n in [0..30]]; // _Vincenzo Librandi_, Jul 18 2011

%K easy,nonn

%O 0,2

%A _Johannes W. Meijer_, Jul 28 2010

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Last modified March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)