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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)):
seq(a(n), n=0..30); # Alois P. Heinz, May 31 2014
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
Sequence in context: A045098 A158310 A031716 * A155019 A020539 A157442
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, May 31 2014
STATUS
approved

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Last modified March 28 13:41 EDT 2024. Contains 371254 sequences. (Running on oeis4.)