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A014632
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Odd pentagonal numbers.
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3
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1, 5, 35, 51, 117, 145, 247, 287, 425, 477, 651, 715, 925, 1001, 1247, 1335, 1617, 1717, 2035, 2147, 2501, 2625, 3015, 3151, 3577, 3725, 4187, 4347, 4845, 5017, 5551, 5735, 6305, 6501, 7107, 7315, 7957, 8177, 8855, 9087, 9801, 10045, 10795, 11051, 11837
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
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FORMULA
| a(n) = a(n-1) +2*a(n-2) -2*a(n-3) -a(n-4) +a(n-5).
a(n) = 48+2*a(n-2)-a(n-4). [Ant King, Aug 16 2011]
G.f.: (1+4*x+28*x^2+8*x^3+7*x^4)/((1+x)^2*(1-x)^3). [From R. J. Mathar, Jul 25 2009]
a(n)=1/8*(11+3*(-1)^(n+1)-12*(n+1))*(3+(-1)^(n+1)-4*(n+1)). [Ant King, Aug 16 2011]
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MATHEMATICA
| Select[Table[n (3n-1)/2, {n, 100}], OddQ] (* From Harvey P. Dale, Feb. 3, 2011 *)
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PROG
| (MAGMA) [1/8*(11+3*(-1)^(n+1)-12*(n+1))*(3+(-1)^(n+1)-4*(n+1)): n in [0..40]]; // Vincenzo Librandi, Aug 17 2011
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CROSSREFS
| Sequence in context: A199584 A087675 A128044 * A117985 A115707 A117793
Adjacent sequences: A014629 A014630 A014631 * A014633 A014634 A014635
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KEYWORD
| nonn
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AUTHOR
| Mohammad K. Azarian (ma3(AT)evansville.edu)
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EXTENSIONS
| More terms from Patrick De Geest (pdg(AT)worldofnumbers.com)
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