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a(n) = 7*n - a(n-1), with a(1) = 1.
8

%I #34 Aug 03 2024 07:16:17

%S 1,13,8,20,15,27,22,34,29,41,36,48,43,55,50,62,57,69,64,76,71,83,78,

%T 90,85,97,92,104,99,111,106,118,113,125,120,132,127,139,134,146,141,

%U 153,148,160,155,167,162,174,169,181,176,188,183,195,190,202,197,209,204

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

%H Harvey P. Dale, <a href="/A166522/b166522.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 G.f.: x*(1+12*x-6*x^2) / ( (1+x)*(1-x)^2 ). - _R. J. Mathar_, Mar 08 2011

%F a(n) = a(n-1) + a(n-2) - a(n-3), a(1)=1, a(2)=13, a(3)=8. - _Harvey P. Dale_, Jun 07 2012

%F E.g.f.: (1/4)*(17*exp(-x) + 7*(1 + 2*x)*exp(x) - 24). - _G. C. Greubel_, May 16 2016

%F a(n) = (1/4)*(14*n + 7 + 17*(-1)^n). - _G. C. Greubel_, Aug 03 2024

%t RecurrenceTable[{a[1]==1,a[n]==7n-a[n-1]},a,{n,60}] (* or *) LinearRecurrence[{1,1,-1},{1,13,8},60] (* _Harvey P. Dale_, Jun 07 2012 *)

%o (Magma)

%o A166522:= func< n | ( 7*n -5 +17*((n+1) mod 2) )/2 >;

%o [A166522(n): n in [1..100]]; // _G. C. Greubel_, Aug 03 2024

%o (SageMath)

%o def A166522(n): return ( 7*n -5 +17*((n+1)%2) )//2

%o [A166522(n) for n in range(1,101)] # _G. C. Greubel_, Aug 03 2024

%Y Cf. A166519, A166520, A166521, A166523, A166524, A166525, A166526.

%K nonn,easy

%O 1,2

%A _Vincenzo Librandi_, Oct 16 2009