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A103454 a(n) = 0^n + 4^n - 1. 2
1, 3, 15, 63, 255, 1023, 4095, 16383, 65535, 262143, 1048575, 4194303, 16777215, 67108863, 268435455, 1073741823, 4294967295, 17179869183, 68719476735, 274877906943, 1099511627775, 4398046511103, 17592186044415, 70368744177663 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A transform of 4^n under the matrix A103452.

The square of the cotangent of the arcsin of 1/(2^n). - Al Hakanson (hawkuu(AT)excite.com), Feb 23 2006

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (5,-4).

FORMULA

G.f.: (1 - 2*x + 4*x^2)/((1-x)*(1-4*x));

a(n) = Sum_{k=0..n} A103452(n, k)*4^k;

a(n) = Sum_{k=0..n} (2*0^(n-k) - 1)*0^(k*(n-k))4^k.

a(n) = A024036(n), n > 0. - R. J. Mathar, Aug 30 2008

PROG

(MAGMA) [0^n+4^n-1: n in [0..30]]; // Vincenzo Librandi, Jul 02 2011

CROSSREFS

Sequence in context: A218366 A218236 A218282 * A024036 A111303 A118339

Adjacent sequences:  A103451 A103452 A103453 * A103455 A103456 A103457

KEYWORD

easy,nonn,changed

AUTHOR

Paul Barry, Feb 06 2005

STATUS

approved

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Last modified October 21 06:25 EDT 2018. Contains 316405 sequences. (Running on oeis4.)