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Search: id:A109613
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| 1, 1, 3, 3, 5, 5, 7, 7, 9, 9, 11, 11, 13, 13, 15, 15, 17, 17, 19, 19, 21, 21, 23, 23, 25, 25, 27, 27, 29, 29, 31, 31, 33, 33, 35, 35, 37, 37, 39, 39, 41, 41, 43, 43, 45, 45, 47, 47, 49, 49, 51, 51, 53, 53, 55, 55, 57, 57, 59, 59, 61, 61, 63, 63, 65, 65, 67, 67, 69, 69, 71, 71, 73
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n) = A052928(n) + 1 = 2*A004526(n) + 1.
a(n) = A028242(n) + A110654(n).
Diagonal sums of number triangle A113126. - Paul Barry (pbarry(AT)wit.ie), Oct 14 2005
When partitioning a convex n-gon by all the diagonals, the maximum number of sides in resulting polygons is 2*floor(n/2)+1 = a(n-1) (from Moscow Olympiad problem 1950) - Tanya Khovanova (tanyakh(AT)yahoo.com), Apr 06 2008
Its ordinal transform is A000034 [From Paolo P. Lava (ppl(AT)spl.at), Jun 25 2009]
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Nov 12 2009: (Start)
The inverse values of the coefficients in the series expansion of f(x) = (1/2)*(1+x)*ln((1+x)/(1-x)) lead to this sequence; cf. A098557.
(End)
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FORMULA
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a(n) = 2*floor(n/2) + 1.
a(n) = A052938(n-2) + A084964(n-2) for n>1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 27 2005
G.f.: (1+x+x^2+x^3)/(1-x^2)^2; - Paul Barry (pbarry(AT)wit.ie), Oct 14 2005
a(n)=n+[1+(-1)^n]/2, with n>=0 - Paolo P. Lava (ppl(AT)spl.at), May 08 2007
a(n)=2*a(n-2)-a(n-4); a(0)=1, a(1)=1, a(2)=3, a(3)=3. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 03 2008]
a(n)=A001477(n)+A059841(n). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 31 2009]
a(n)=2*n-a(n-1)-2 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 21 2009]
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EXAMPLE
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For n=2, a(2)=2*2-1-2=1; n=3, a(3)=2*3-1-2=3; n=4, a(4)=2*4-3-2=3 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 21 2009]
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CROSSREFS
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Cf. A063196, A110660.
Sequence in context: A117767 A063196 A127630 this_sequence A073737 A133908 A111213
Adjacent sequences: A109610 A109611 A109612 this_sequence A109614 A109615 A109616
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KEYWORD
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nonn,new
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 01 2005
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