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A078633
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Smallest number of sticks of length 1 needed to construct n squares with sides of length 1.
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8
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4, 7, 10, 12, 15, 17, 20, 22, 24, 27, 29, 31, 34, 36, 38, 40, 43, 45, 47, 49, 52, 54, 56, 58, 60, 63, 65, 67, 69, 71, 74, 76, 78, 80, 82, 84, 87, 89, 91, 93, 95, 97, 100, 102, 104, 106, 108, 110, 112, 115, 117, 119, 121, 123, 125, 127, 130, 132, 134, 136, 138, 140, 142
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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A182834(a(n)) mod 2 = 0, or, where even terms occur in A182834. - Reinhard Zumkeller, Aug 05 2014
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Ralph H. Buchholz and Warwick De Launey, The square, the triangle and the hexagon, 1996.
Douglas A. Torrance, Enumeration of planar Tangles, arXiv:1906.01541 [math.CO], 2019.
Douglas A. Torrance, Enumeration of planar Tangles, Proc. Math. Sci. 130 (50 (2020)
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FORMULA
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a(n) = 2*n + ceiling(2*sqrt(n)) = 2*n + A027434(n).
a(n) = (4*n + A027709(n))/2. - Tanya Khovanova, Mar 07 2008
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EXAMPLE
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a(2)=7 because we have following construction:
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MATHEMATICA
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Table[2n+Ceiling[2Sqrt[n]], {n, 70}] (* Harvey P. Dale, Jun 20 2011 *)
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PROG
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(Haskell)
a078633 n = 2 * n + ceiling (2 * sqrt (fromIntegral n))
-- Reinhard Zumkeller, Aug 05 2014
(PARI) a(n) = 2*n + ceil(2*sqrt(n)); \\ Michel Marcus, Mar 26 2018
(Python)
from math import isqrt
def A078633(n): return (m:=n<<1)+1+isqrt((m<<1)-1) # Chai Wah Wu, Jul 28 2022
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CROSSREFS
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Cf. A027434, A027709, A135708, A182834.
Sequence in context: A310675 A176292 A050173 * A190008 A184911 A103762
Adjacent sequences: A078630 A078631 A078632 * A078634 A078635 A078636
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Mambetov Timur and Takenov Nurdin (timur_teufel(AT)mail.ru), Dec 12 2002
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STATUS
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approved
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