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a(n) = 6 + 10*floor((n-1)/2).
1

%I #34 Sep 08 2022 08:45:49

%S 6,6,16,16,26,26,36,36,46,46,56,56,66,66,76,76,86,86,96,96,106,106,

%T 116,116,126,126,136,136,146,146,156,156,166,166,176,176,186,186,196,

%U 196,206,206,216,216,226,226,236,236,246,246,256,256,266,266,276,276,286

%N a(n) = 6 + 10*floor((n-1)/2).

%H Vincenzo Librandi, <a href="/A168460/b168460.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 a(n) = 10*n - a(n-1) - 8, with n>1, a(1)=6.

%F From _R. J. Mathar_, Jan 04 2011: (Start)

%F a(n) = 2*A168283(n).

%F a(n+1) = A017341(floor(n/2)).

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

%F a(n) = a(n-1) + a(n-2) - a(n-3) for n>3. - _Vincenzo Librandi_, Sep 19 2013

%F From _G. C. Greubel_, Jul 23 2016: (Start)

%F a(n) = (10*n - 5*(-1)^n - 3)/2.

%F E.g.f.: (1/2)*(-5 + 8*exp(x) + (10*x - 3)*exp(2*x))*exp(-x). (End)

%F a(n) = a(n-2) + 10 for n>2. - _Wesley Ivan Hurt_, Jul 24 2016

%p A168460:=n->6 + 10*floor((n-1)/2): seq(A168460(n), n=1..100); # _Wesley Ivan Hurt_, Jul 24 2016

%t RecurrenceTable[{a[1]==6,a[n]==10n-a[n-1]-8},a,{n,80}] (* or *) LinearRecurrence[{1,1,-1},{6,6,16},80] (* _Harvey P. Dale_, Apr 25 2011 *)

%t Table[6 + 10 Floor[(n - 1)/2], {n, 70}] (* or *) CoefficientList[Series[2 (3 + 2 x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* _Vincenzo Librandi_, Sep 19 2013 *)

%o (Magma) [6+10*Floor((n-1)/2): n in [1..70]]; // _Vincenzo Librandi_, Sep 19 2013

%Y Cf. A017341, A168283.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Nov 26 2009

%E New definition by _Vincenzo Librandi_, Sep 19 2013