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Search: id:A085046
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| A085046 |
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a(1) = 1, a(2) = 3, then a(2n) = (a(2n-1)*a(2n+1))^1/2 and a(2n+1) = {a(2n) + a(2n+2)}/2. Even positioned terms are the geometric mean and odd positioned terms are the arithmetic mean of their neighbors. |
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3
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| 1, 3, 9, 15, 25, 35, 49, 63, 81, 99, 121, 143, 169, 195, 225, 255, 289, 323, 361, 399, 441, 483, 529, 575, 625, 675, 729, 783, 841, 899, 961, 1023, 1089, 1155, 1225, 1295, 1369, 1443, 1521, 1599, 1681, 1763, 1849, 1935, 2025, 2115, 2209, 2303, 2401, 2499, 2601
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Sequence pattern looks like this 1*1,1*3,3*3,3*5,5*5,5*7,7*7,7*9,9*9,9*11,11*11,...
a(n) is also the longest path, in number of cells, between diagonally opposite corners of an n X n matrix if diagonal movement between adjacent cells is not allowed and no cell is used more than once. - Ray G. Opao (1260(AT)email.com), Jul 02 2007
(-1)^n*a(n) appears to be the Hankel transform of A141222. - Paul Barry (pbarry(AT)wit.ie), Jun 14 2008
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FORMULA
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a(2n+1) = (2n+1)^2 and a(2n) = 4n^2 -1.
a(n+1) is the determinant of the n X n matrix M_(i, i)=3, M_(i, j)=2 if (i+j) is even, M_(i, j)=0 if (i+j) is odd. - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 06 2003
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CROSSREFS
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A008811(2n)-1.
Sequence in context: A058972 A026222 A099989 this_sequence A138495 A055927 A087031
Adjacent sequences: A085043 A085044 A085045 this_sequence A085047 A085048 A085049
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy and Meenakshi Srikanth (amarnath_murthy(AT)yahoo.com), Jun 20 2003
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EXTENSIONS
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More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 06 2003
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