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Search: id:A060626
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| A060626 |
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Number of right triangles of a given area required to form successively larger squares. |
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+0
2
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| 2, 14, 34, 62, 98, 142, 194, 254, 322, 398, 482, 574, 674, 782, 898, 1022, 1154, 1294, 1442, 1598, 1762, 1934, 2114, 2302, 2498, 2702, 2914, 3134, 3362, 3598, 3842, 4094, 4354, 4622, 4898, 5182, 5474, 5774, 6082, 6398, 6722, 7054, 7394, 7742, 8098, 8462
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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a(n) = number of row of Pascal's triangle in which three consecutive entries appear in the ratio n : n+1 : n+2 (valid for n = 0 if you consider a position of -1 to have value 0). E.g. entries in the ratio 1:2:3 appear in row 14 (1001, 2002, 3003); entries in the ratio 2:3:4 appear in row 34 (927983760, 1391975640, 1855967520); and so on. (The position within the row is given by A091823). - Howard A. Landman (howard(AT)riverrock.org), Mar 08 2004
a(n)*(a(n)+1) is an oblong number (Cf. A002378) with the property that the product with the oblong numbers n*(n+1) or (n+1)*(n+2) both are again oblong numbers. Example: For n=3 we have (62*63)*(3*4)=216*217 and (62*63)*(4*5)=279*280 - Herbert Kociemba (kociemba(AT)t-online.de), Apr 13 2008
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FORMULA
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a(n) = 4*n^2+8*n+2.
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MAPLE
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for n from 0 to 80 do printf(`%d, `, 4*n^2+8*n+2) od:
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MATHEMATICA
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lst={}; Do[AppendTo[lst, 4*n^2+8*n+2], {n, 0, 5!}]; lst...and/or... s=-2; lst={}; Do[s+=n+1; AppendTo[lst, s], {n, 3, 6!, 8}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 25 2008]
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CROSSREFS
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Cf. A007318, A091823.
Cf. A002378.
Sequence in context: A083015 A050591 A073535 this_sequence A096311 A034842 A145910
Adjacent sequences: A060623 A060624 A060625 this_sequence A060627 A060628 A060629
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KEYWORD
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easy,nonn
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AUTHOR
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Jason Earls (zevi_35711(AT)yahoo.com), Apr 13 2001
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 14 2001
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