OFFSET
0,3
COMMENTS
Chebyshev polynomial of the first kind T(10,n).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1).
FORMULA
G.f.: (-1 + 12*x + 262021*x^2 + 19736800*x^3 + 223070134*x^4 + 685903960*x^5 + 685903498*x^6 + 223070464*x^7 + 19736635*x^8 + 262076*x^9 + x^10)/(1 - x)^11.
a(n) = (2*n^2 - 1)*(256*n^8 - 512*n^6 + 304*n^4 - 48*n^2 + 1).
a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11). - Wesley Ivan Hurt, May 04 2024
MAPLE
a:= n-> simplify(ChebyshevT(10, n)):
seq(a(n), n=0..30); # Alois P. Heinz, May 31 2014
MATHEMATICA
Table[ChebyshevT[10, n], {n, 0, 30}] (* or *) Table[512 n^10 - 1280 n^8 + 1120 n^6 - 400 n^4 + 50 n^2 - 1, {n, 0, 30}]
PROG
(Magma) [512*n^10-1280*n^8+1120*n^6-400*n^4+50*n^2-1: n in [0..30]];
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Vincenzo Librandi, May 31 2014
STATUS
approved