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A161168
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a(n) = 2^n + 4^n.
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7
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2, 6, 20, 72, 272, 1056, 4160, 16512, 65792, 262656, 1049600, 4196352, 16781312, 67117056, 268451840, 1073774592, 4295032832, 17180000256, 68719738880, 274878431232, 1099512676352, 4398048608256, 17592190238720, 70368752566272
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OFFSET
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0,1
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COMMENTS
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a(n) written in base 2: a(0) = 10, a(n) for n >= 1: 110, 10100, 1001000, 100010000, ..., i.e., number 1, (n-1) times 0, number 1, n times 0 (see A163664). a(n) is a bisection of A005418. - Jaroslav Krizek, Aug 14 2009
For n > 0 let 2^(n+1) be the length of the even leg of a primitive Pythagorean triangle (PPT); then the odd leg is constrained to have a length of 4^n-1 and the hypotenuse to have a length of 4^n+1. The resulting triangle has a semiperimeter of 4^n + 2^n. - Frank M Jackson, Dec 28 2017
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LINKS
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FORMULA
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G.f.: -2*(3*x-1) / ((2*x-1)*(4*x-1)). - Colin Barker, Mar 19 2013
E.g.f.: e^(2*x) + e^(4*x). - Iain Fox, Dec 28 2017
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MAPLE
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MATHEMATICA
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PROG
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(Sage) [2^n + 4^n for n in range(0, 25)]
(Sage) [sigma(4, n)-1for n in range(0, 25)]
(Magma) [ 2^n+4^n: n in [0..25] ];
(PARI) first(n) = Vec(2*(1 - 3*x)/((1 - 2*x)*(1 - 4*x)) + O(x^n)) \\ Iain Fox, Dec 28 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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