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A168212 a(n) = 7*n - a(n-1) + 1 with n>1, a(1)=4. 3

%I #23 Sep 08 2022 08:45:48

%S 4,11,11,18,18,25,25,32,32,39,39,46,46,53,53,60,60,67,67,74,74,81,81,

%T 88,88,95,95,102,102,109,109,116,116,123,123,130,130,137,137,144,144,

%U 151,151,158,158,165,165,172,172,179,179,186,186,193,193,200,200,207,207

%N a(n) = 7*n - a(n-1) + 1 with n>1, a(1)=4.

%H Vincenzo Librandi, <a href="/A168212/b168212.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).

%F From _R. J. Mathar_, Nov 22 2009: (Start)

%F a(n) = a(n-1) +a(n-2) -a(n-3).

%F a(n) = (9 + 14*n + 7*(-1)^n)/4.

%F G.f.: x*(4 + 7*x - 4*x^2)/((1+x)* (x-1)^2). (End)

%F E.g.f.: (1/4)*(7 - 16*exp(x) + (9 + 14*x)*exp(2*x))*exp(-x). - _G. C. Greubel_, Jul 15 2016

%t LinearRecurrence[{1, 1, -1}, {4, 11, 11}, 60] (* _Vincenzo Librandi_, Feb 28 2012 *)

%t Join[{4},With[{c=LinearRecurrence[{2,-1},{11,18},50]},Riffle[c,c]]] (* or *) With[{c=7*Range[0,50]+4},Rest[Riffle[c,c]]] (* _Harvey P. Dale_, May 09 2018 *)

%o (Magma) I:=[4, 11, 11]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Feb 28 2012

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Nov 20 2009

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Last modified March 28 16:58 EDT 2024. Contains 371254 sequences. (Running on oeis4.)