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Search: id:A144396
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| A144396 |
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The odd numbers greater than 1. |
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+0
9
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| 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Last number of the n-th row of the triangle described in A142717.
If negated, these are also the values at local minima of the sequence A141620.
a(n)=sqrt(8n+1) when n is a triangular number (1, 3, 6, etc) [A000217] [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Jan 11 2009]
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FORMULA
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Except for the first term of [A002378], if X=[A144396], Y=[A007395], A= [A002378], we have, for all other terms, Pell's equation: [A144396]^2 - [A002378]*[A007395]^2=1; (X^2-A*Y^2=1); example: 3^2-2*2^2=1; 5^2-6*2^2=1; 19^2-90*2^2=1, and so on. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 11 2009]
a(n)=A005408(n+1)=A000290(n+1)-A000290(n).
G.f.: x*(3-x)/(1-x)^2 [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Aug 30 2009]
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CROSSREFS
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Cf. A000217 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Jan 11 2009]
Cf. A002378, A007395 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 11 2009]
Sequence in context: A157142 A004273 A005408 this_sequence A060747 A089684 A105356
Adjacent sequences: A144393 A144394 A144395 this_sequence A144397 A144398 A144399
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KEYWORD
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nonn,less,easy
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AUTHOR
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Paul Curtz (bpcrtz(AT)free.fr), Oct 03 2008
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EXTENSIONS
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Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 21 2009
More terms from Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jun 27 2009
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