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A157870
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a(n) = (4n+1)(4n+2) = (4n+2)!/(4n)!.
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2
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2, 30, 90, 182, 306, 462, 650, 870, 1122, 1406, 1722, 2070, 2450, 2862, 3306, 3782, 4290, 4830, 5402, 6006, 6642, 7310, 8010, 8742, 9506, 10302, 11130, 11990, 12882, 13806, 14762, 15750, 16770, 17822, 18906, 20022, 21170, 22350, 23562, 24806, 26082, 27390, 28730, 30102, 31506, 32942
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OFFSET
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0,1
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COMMENTS
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I was trying to prove the irrationality of pi and I encountered this sequence.
A014634 * 2 = A157870. A157870 / 2 = A014634. [From Vladimir Joseph Stephan Orlovsky, Mar 10 2009]
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for sequences related to linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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a(n)=A002378(4n+1)=2*A014634(n). [R. J. Mathar, Mar 11 2009]
G.f.: 2*(1+12*x+3*x^2)/(1-x)^3. - Vincenzo Librandi, Jul 10 2012
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Vincenzo Librandi, Jul 10 2012
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MATHEMATICA
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lst={}; Do[a=(2*n+1)*(4*n+1)*2; AppendTo[lst, a], {n, 0, 5!}]; lst [From Vladimir Joseph Stephan Orlovsky, Mar 10 2009]
Table[(4n+1)*(4n+2), {n, 0, 50}] (* Vincenzo Librandi, Jul 10 2012 *)
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PROG
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(MAGMA) (4*n+1)*(4*n+2). // Vincenzo Librandi Jul 10 2012
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CROSSREFS
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Sequence in context: A189100 A085637 A193177 * A078838 A089288 A154413
Adjacent sequences: A157867 A157868 A157869 * A157871 A157872 A157873
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KEYWORD
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nonn,easy
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AUTHOR
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SUNKU Sai Swaroop (sai2020(AT)gmail.com), Mar 08 2009
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EXTENSIONS
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Corrected definition and extended by R. J. Mathar, Mar 11 2009
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STATUS
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approved
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