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A155196 a(n)=7*a(n-1)+a(n-2), n>2 ; a(0)=1, a(1)=6, a(2)=42 . 1

%I

%S 1,6,42,300,2142,15294,109200,779694,5567058,39749100,283810758,

%T 2026424406,14468781600,103307895606,737624050842,5266676251500,

%U 37604357811342,268497180930894,1917084624327600,13688089551224094

%N a(n)=7*a(n-1)+a(n-2), n>2 ; a(0)=1, a(1)=6, a(2)=42 .

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7, 1).

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

%F a(n)=3*{[(7/2)+(1/2)*sqrt(53)]^(n-1)+[(7/2)-(1/2)*sqrt(53)]^(n-1)}+(21/53)*sqrt(53)*{[(7/2)+(1/2)*sqrt(53)]^(n-1)-[(7/2)-(1/2)*sqrt(53)]^(n-1)}+[C(2*n,n) mod 2], with n>=0 [From _Paolo P. Lava_, Jan 26 2009]

%F a(n) = Sum_{k, 0<=k<=n} A155161(n,k)*6^k. - _Philippe Deléham_, Feb 08 2012

%t Join[{1},LinearRecurrence[{7,1},{6,42},20]] (* _Harvey P. Dale_, Sep 04 2014 *)

%K nonn,easy

%O 0,2

%A _Philippe Deléham_, Jan 21 2009

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Last modified June 14 09:06 EDT 2021. Contains 345018 sequences. (Running on oeis4.)