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a(n) = (7^n+14*(-8)^n)/15.
3

%I #10 Jun 30 2023 14:29:59

%S 1,-7,63,-455,3983,-29463,252511,-1902439,16043055,-122579639,

%T 1020990719,-7885450503,65060930767,-506646158935,4150058281887,

%U -32522243182247,264925506967919,-2086171125173751,16921999515377215

%N a(n) = (7^n+14*(-8)^n)/15.

%H G. C. Greubel, <a href="/A166153/b166153.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 (-1, 56).

%F a(n) = 56*a(n-2)-a(n-1), a(0)= 1, a(1)= -7, for n>1.

%F G.f.: (1-6*x)/(1+x-56*x^2).

%F a(n) = Sum_{k=0..n} A112555(n,k)*(-8)^k.

%F E.g.f.: (1/15)*(exp(7*x) + 14*exp(-8*x)). - _G. C. Greubel_, May 01 2016

%t LinearRecurrence[{-1, 56}, {1, -7}, 50] (* _G. C. Greubel_, May 01 2016 *)

%Y Cf. A112555, A166035, A166036, A166149, A166152.

%K easy,sign

%O 0,2

%A _Philippe Deléham_, Oct 08 2009