A243131 a(n) = 16*n^5 - 20*n^3 + 5*n.

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

Offset: 0

Author

Vincenzo Librandi, May 31 2014

Keywords

• nonn
• easy

Comments

Chebyshev polynomial of the first kind T(5,n).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A056220, A144129, A144130.

Programs

Magma

[16*n^5-20*n^3+5*n: n in [0..40]];

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 *)

PARI

apply(x->polchebyshev(5,1,x), vector(30,i,i-1)) \\ Hugo Pfoertner, Oct 18 2022

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.