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A078633 Smallest number of sticks of length 1 needed to construct n squares with sides of length 1. 8
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)
OFFSET

1,1

COMMENTS

A182834(a(n)) mod 2 = 0, or, where even terms occur in A182834. - Reinhard Zumkeller, Aug 05 2014

LINKS

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.

FORMULA

a(n) = 2*n + ceiling(2*sqrt(n)) = 2*n + A027434(n).

a(n) = (4*n + A027709(n))/2. - Tanya Khovanova, Mar 07 2008

EXAMPLE

a(2)=7 because we have following construction:

   _ _

  |_|_|

MATHEMATICA

Table[2n+Ceiling[2Sqrt[n]], {n, 70}] (* Harvey P. Dale, Jun 20 2011 *)

PROG

(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

CROSSREFS

Cf. A027434, A027709, A135708, A182834.

Sequence in context: A310675 A176292 A050173 * A190008 A184911 A103762

Adjacent sequences:  A078630 A078631 A078632 * A078634 A078635 A078636

KEYWORD

nonn,easy,nice

AUTHOR

Mambetov Timur and Takenov Nurdin (timur_teufel(AT)mail.ru), Dec 12 2002

STATUS

approved

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Last modified August 13 22:57 EDT 2020. Contains 336473 sequences. (Running on oeis4.)