|
| |
|
|
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).
|
|
1
|
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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: A102876 A188166 A184220 * A316735 A010922 A010902
Adjacent sequences: A026062 A026063 A026064 * A026066 A026067 A026068
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Clark Kimberling
|
|
|
STATUS
|
approved
|
| |
|
|
