A190787 Odd powers of 2 and 9 times odd powers of 2, sorted.

2, 8, 18, 32, 72, 128, 288, 512, 1152, 2048, 4608, 8192, 18432, 32768, 73728, 131072, 294912, 524288, 1179648, 2097152, 4718592, 8388608, 18874368, 33554432, 75497472, 134217728, 301989888, 536870912, 1207959552, 2147483648, 4831838208, 8589934592, 19327352832, 34359738368, 77309411328, 137438953472, 309237645312

Offset

1,1

Links

Table of n, a(n) for n=1..37.

Index entries for linear recurrences with constant coefficients, signature (0, 4).

Formula

G.f.: 2*x*(1+4*x+5*x^2)/(1-4*x^2). - Mark Thomas

From Ilya Gutkovskiy, Jul 22 2016: (Start)

E.g.f.: (-8 - 10*x + 9*sinh(2*x) + 8*cosh(2*x))/4.

a(n) = 2^(n-3)*(17 - (-1)^n), for n>1. (End)

Example

32 = 2^5 is in the sequence (since the exponent 5 is odd), and 72 = 9*2^3 is also in the sequence. - Michael B. Porter, Jul 22 2016

Mathematica

nn = 10^12; Union@ Flatten@ {#, TakeWhile[9 #, # <= nn &]} &[2^Range[1, Floor[Log2[nn]], 2]] (* or *)
Rest@ CoefficientList[Series[2 x (1 + 4 x + 5 x^2)/(1 - 4 x^2), {x, 0, 37}], x] (* Michael De Vlieger, Jul 22 2016 *)

Crossrefs

Sequence in context: A050804 A081324 A361903 * A018229 A365265 A166830

Adjacent sequences: A190784 A190785 A190786 * A190788 A190789 A190790

Keyword

nonn

Author

N. J. A. Sloane, May 19 2011, following a suggestion by Mark Thomas.

Status

approved