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A190787 Odd powers of 2 and 9 times odd powers of 2, sorted. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

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: A051787 A050804 A081324 * A018229 A166830 A072779

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

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Last modified July 10 12:34 EDT 2020. Contains 335576 sequences. (Running on oeis4.)