A084181 2^n+(-2)^n-(-1)^n.

1, 1, 7, 1, 31, 1, 127, 1, 511, 1, 2047, 1, 8191, 1, 32767, 1, 131071, 1, 524287, 1, 2097151, 1, 8388607, 1, 33554431, 1, 134217727, 1, 536870911, 1, 2147483647, 1, 8589934591, 1, 34359738367, 1, 137438953471, 1, 549755813887, 1, 2199023255551

Offset

0,3

Comments

Binomial transform is A084182.

Links

Table of n, a(n) for n=0..40.

Index entries for linear recurrences with constant coefficients, signature (-1,4,4).

Formula

a(n)=2^n+(-2)^n-(-1)^n;

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

E.g.f.: exp(2x)-exp(-x)+exp(-2x).

Mathematica

LinearRecurrence[{-1, 4, 4}, {1, 1, 7}, 50] (* or *) Riffle[ LinearRecurrence[ {5, -4}, {1, 7}, 30], 1] (* Harvey P. Dale, Jan 02 2019 *)

Crossrefs

Cf. A083420.

Sequence in context: A301731 A379007 A228498 * A002678 A147482 A171770

Adjacent sequences: A084178 A084179 A084180 * A084182 A084183 A084184

Keyword

easy,nonn

Author

Paul Barry, May 19 2003

Status

approved