|
|
A243131
|
|
a(n) = 16*n^5 - 20*n^3 + 5*n.
|
|
2
|
|
|
0, 1, 362, 3363, 15124, 47525, 120126, 262087, 514088, 930249, 1580050, 2550251, 3946812, 5896813, 8550374, 12082575, 16695376, 22619537, 30116538, 39480499, 51040100, 65160501, 82245262, 102738263, 127125624, 155937625, 189750626, 229188987
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Chebyshev polynomial of the first kind T(5,n).
|
|
LINKS
|
|
|
FORMULA
|
a(n) = n*(16*n^4-20*n^2+5) = (-1/4)*n *(-8*n^2+5+sqrt(5))*(8*n^2-5+sqrt(5)).
G.f.: x*(1 + 356*x + 1206*x^2 + 356*x^3 + x^4)/(1 - x)^6.
|
|
MAPLE
|
a:= n-> simplify(ChebyshevT(5, n)):
|
|
MATHEMATICA
|
Table[ChebyshevT[5, n], {n, 0, 40}] (* or *) Table[16*n^5 - 20*n^3 + 5*n, {n, 0, 20}]
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 1, 362, 3363, 15124, 47525}, 30] (* Harvey P. Dale, Aug 03 2023 *)
|
|
PROG
|
(Magma) [16*n^5-20*n^3+5*n: n in [0..40]];
(PARI) apply(x->polchebyshev(5, 1, x), vector(30, i, i-1)) \\ Hugo Pfoertner, Oct 18 2022
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|