A020537 a(n) = 4*8^n - 3*2^n.

1, 26, 244, 2024, 16336, 130976, 1048384, 8388224, 67108096, 536869376, 4294964224, 34359732224, 274877894656, 2199023230976, 17592185995264, 140737488257024, 1125899906646016, 9007199254347776, 72057594037141504, 576460752301850624, 4611686018424242176

Offset

0,2

Comments

3rd Chebyshev polynomial (first kind) evaluated at powers of 2.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (10,-16).

Formula

a(n) = 10*a(n-1)-16*a(n-2). - Colin Barker, May 03 2015

G.f.: (16*x+1) / ((2*x-1)*(8*x-1)). - Colin Barker, May 03 2015

Maple

with(orthopoly):seq(T(3, 2^i), i=0..24);

Mathematica

Table[ChebyshevT[3, 2^n], {n, 1, 40}] (* Vladimir Joseph Stephan Orlovsky, Nov 03 2009 *)

Prog

(PARI) a(n) = polchebyshev(3, 1, 2^n); \\ Michel Marcus, Dec 28 2014
(PARI) Vec((16*x+1)/((2*x-1)*(8*x-1)) + O(x^100)) \\ Colin Barker, May 03 2015

Crossrefs

Sequence in context: A293614 A245873 A275880 * A184461 A088889 A348490

Adjacent sequences: A020534 A020535 A020536 * A020538 A020539 A020540

Keyword

nonn,easy

Author

Simon Plouffe

Status

approved