A026065 a(n) = (d(n)-r(n))/5, where d = A026063 and r is the periodic sequence with fundamental period (1,4,0,0,0).

14, 23, 36, 51, 69, 90, 114, 143, 175, 211, 251, 295, 345, 399, 458, 522, 591, 667, 748, 835, 928, 1027, 1134, 1247, 1367, 1494, 1628, 1771, 1921, 2079, 2245, 2419, 2603, 2795, 2996, 3206, 3425, 3655, 3894, 4143, 4402, 4671, 4952, 5243, 5545, 5858, 6182, 6519, 6867, 7227, 7599, 7983, 8381

Offset: 6

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,1,-3,3,-1).

Crossrefs

Cf. A152898.

Programs

Mathematica

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

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

Formula

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

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]