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1, 11, 41, 91, 161, 251, 361, 491, 641, 811, 1001, 1211, 1441, 1691, 1961, 2251, 2561, 2891, 3241, 3611, 4001, 4411, 4841, 5291, 5761, 6251, 6761, 7291, 7841, 8411, 9001, 9611, 10241, 10891, 11561, 12251, 12961, 13691, 14441, 15211, 16001, 16811, 17641
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Sequence found by reading the segment (1, 11) together with the line from 11, in the direction 11, 41,..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. - Omar E. Pol, Sep 10 2011
The identity (10n^2+1)^2-(25n^2+5)*(2n)^2=1 can be written as a(n)^2-A158445(n)*A005843(n)^2=1. - Vincenzo Librandi, Jan 03 2012
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| a(n) = A033583(n) + 1.
For n>0: a(n) = A010010(n)/2.
Contribution by Vincenzo Librandi, Jan 03 2012: (Start)
G.f: x*(11+8*x+x^2)/(1-x)^3.
a(n) = a(-n) = 3*a(n-1) -3*a(n-2) +a(n-3). (End)
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MATHEMATICA
| Table[10*n^2+1, {n, 0, 50}] (* Vincenzo Librandi, Jan 03 2012 *)
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CROSSREFS
| Cf. A158445, A005843 [From Vincenzo Librandi, Mar 19 2009]
Sequence in context: A031389 A178495 A097991 * A065145 A030685 A132208
Adjacent sequences: A158184 A158185 A158186 * A158188 A158189 A158190
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KEYWORD
| nonn,easy
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 13 2009
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