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a(n) = 8 * A104720(n) + ceiling(n/2).
1

%I #20 Apr 11 2019 17:06:47

%S 8,89,897,8978,89786,897867,8978675,89786756,897867564,8978675645,

%T 89786756453,897867564534,8978675645342,89786756453423,

%U 897867564534231,8978675645342312,89786756453423120,897867564534231201,8978675645342312009,89786756453423120090,897867564534231200898,8978675645342312008979

%N a(n) = 8 * A104720(n) + ceiling(n/2).

%H Colin Barker, <a href="/A319842/b319842.txt">Table of n, a(n) for n = 0..900</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (11,-9,-11,10).

%F a(n) = (198*n - 243*(-1)^n + 2^(n+8)*5^(n+3) - 3245)/3564.

%F From _Colin Barker_, Sep 29 2018: (Start)

%F G.f.: (8 + x - 10*x^2) / ((1 - x)^2*(1 + x)*(1 - 10*x)).

%F a(n) = 11*a(n-1) - 9*a(n-2) - 11*a(n-3) + 10*a(n-4) for n>3.

%F (End)

%t a[n_]:=(198*n - 243*(-1)^n + 2^(n+8)*5^(n+3) - 3245)/3564; Array[a, 50, 0] (* _Stefano Spezia_, Sep 29 2018 *)

%t LinearRecurrence[{11,-9,-11,10},{8,89,897,8978},40] (* _Harvey P. Dale_, Apr 11 2019 *)

%o (PARI) {a(n) = (198*n-243*(-1)^n+2^(n+8)*5^(n+3)-3245)/3564}

%o (PARI) Vec((8 + x - 10*x^2) / ((1 - x)^2*(1 + x)*(1 - 10*x)) + O(x^25)) \\ _Colin Barker_, Sep 29 2018

%Y Cf. A104720, A110654.

%K nonn,easy

%O 0,1

%A _Seiichi Manyama_, Sep 29 2018