

A143096


a(n) = 2*a(n1)1, with a(1)=1, a(2)=4, a(3)=5.


1



1, 4, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145, 524289, 1048577, 2097153, 4194305, 8388609, 16777217, 33554433, 67108865, 134217729, 268435457, 536870913, 1073741825, 2147483649, 4294967297, 8589934593
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OFFSET

1,2


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..2000
Index entries for linear recurrences with constant coefficients, signature (3,2).


FORMULA

Binomial transform of 0, 1, 2, 4, 9, 13, 20, 26, 35, ... (offset 0).
O.g.f.: x*(1+x5*x^2+2*x^3)/((1x)*(12*x)). a(n) = 1+2^(n1), n>2.  R. J. Mathar, Jul 31 2008
a(n) = A048578(n2), n>=3.  R. J. Mathar, Aug 10 2008


EXAMPLE

a(4) = 9 = 2*a(3)  1 = 2*5  1.
a(4) = 9 = (1, 3, 3, 1) dot (1, 3, 2, 5) = (1 + 9  6 + 5).


MATHEMATICA

Join[{1, 4}, NestList[2#1&, 5, 40]] (* or *) Join[{1, 4}, LinearRecurrence[ {3, 2}, {5, 9}, 40]] (* Harvey P. Dale, Feb 18 2014 *)


CROSSREFS

Cf. A065190.
Sequence in context: A051216 A255978 A069089 * A280225 A153058 A216225
Adjacent sequences: A143093 A143094 A143095 * A143097 A143098 A143099


KEYWORD

nonn,easy


AUTHOR

Gary W. Adamson & Roger L. Bagula, Jul 23 2008


STATUS

approved



