A026065 - OEIS

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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

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OFFSET

6,1

LINKS

Table of n, a(n) for n=6..58.

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

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]

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 *)

PROG

(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

CROSSREFS

Cf. A152898.

Sequence in context: A188166 A184220 A373647 * A316735 A010922 A010902

Adjacent sequences: A026062 A026063 A026064 * A026066 A026067 A026068

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

STATUS

approved