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A005262
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Floor((7*2^(n+1)-9n-10)/3).
(Formerly M2793)
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1
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1, 3, 9, 25, 59, 131, 277, 573, 1167, 2359, 4745, 9521, 19075, 38187, 76413, 152869, 305783, 611615, 1223281, 2446617, 4893291, 9786643, 19573349, 39146765, 78293599
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Arises from Tower of Hanoi problem.
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REFERENCES
| Problem 1169, Crux Mathematicorum, 13 (No. 10, 1987), 328-332.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Index to sequences with linear recurrences with constant coefficients, signature (3,-1,-3,2).
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FORMULA
| G.f.: -(1+x^2+4*x^3)/((x+1)*(2*x-1)*(x-1)^2) = (1+x^2+4*x^3)/(1-3*x+x^2+3*x^3-2*x^4). - S. Plouffe (see MAPLE line) and Bruno Berselli, Jan 12 2012
a(n) = (28*2^n-18n-(-1)^n-21)/6 = (7*2^(n+1)-9n-10)/3-((-1)^n+1)/6. - Bruno Berselli, Jan 12 2012
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MAPLE
| A005262:=-(1+z**2+4*z**3)/((z+1)*(2*z-1)*(z-1)**2); [S. Plouffe in his 1992 dissertation.]
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CROSSREFS
| Sequence in context: A032681 A005209 A112522 * A004255 A101357 A065971
Adjacent sequences: A005259 A005260 A005261 * A005263 A005264 A005265
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Definition corrected by Colin Barker (c.barker(AT)orange.fr), Jan 12 2012
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