%I #26 Oct 21 2022 21:29:18

%S 14,23,36,51,69,90,114,143,175,211,251,295,345,399,458,522,591,667,

%T 748,835,928,1027,1134,1247,1367,1494,1628,1771,1921,2079,2245,2419,

%U 2603,2795,2996,3206,3425,3655,3894,4143,4402,4671,4952,5243,5545,5858,6182,6519,6867,7227,7599,7983,8381

%N a(n) = (d(n)-r(n))/5, where d = A026063 and r is the periodic sequence with fundamental period (1,4,0,0,0).

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,0,1,-3,3,-1).

%F a(n) = (n + 6)*(n^2 + 30*n + 71)/30 - 1/5*(1 + 2/5*5^(1/2)*cos(2*n*Pi/5) + 2/5*2^(1/2)*(5 + 5^(1/2))^(1/2)*sin(2*n*Pi/5) - 2/5*5^(1/2)*cos(4*n*Pi/5) + 2/5*2^(1/2)*(5 - 5^(1/2))^(1/2)*sin(4*n*Pi/5)). - _Richard Choulet_, Dec 14 2008

%F G.f.: (14-19*x+9*x^2-2*x^3+x^4-14*x^5+19*x^6-7*x^7) / ( (x^4+x^3+x^2+x+1)*(x-1)^4 ). - _R. J. Mathar_, Jun 23 2013 [Corrected by _Georg Fischer_, May 18 2019]

%t CoefficientList[Series[(14-19*x+9*x^2-2*x^3+x^4-14*x^5+19*x^6-7*x^7) / ( (x^4+x^3+x^2+x+1)*(x-1)^4), {x, 0, 52}], x] (* _Georg Fischer_, May 18 2019 *)

%t LinearRecurrence[{3,-3,1,0,1,-3,3,-1},{14,23,36,51,69,90,114,143},60] (* _Harvey P. Dale_, Sep 27 2020 *)

%o (PARI) my(x='x+O('x^20)); Vec((14-19*x+9*x^2-2*x^3+x^4-14*x^5+19*x^6-7*x^7) / ((x^4+x^3+x^2+x+1)*(x-1)^4)) \\ _Felix Fröhlich_, May 18 2019

%Y Cf. A152898.

%K nonn,easy

%O 6,1

%A _Clark Kimberling_