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A032527
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Concentric pentagonal numbers: floor( 5*n^2 / 4).
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20
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0, 1, 5, 11, 20, 31, 45, 61, 80, 101, 125, 151, 180, 211, 245, 281, 320, 361, 405, 451, 500, 551, 605, 661, 720, 781, 845, 911, 980, 1051, 1125, 1201, 1280, 1361, 1445, 1531, 1620, 1711, 1805, 1901, 2000, 2101
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Also A033429 and A062786 interleaved - Omar E. Pol, Sep 28 2011
Partial sums of A047209. [Reinhard Zumkeller, Jan 07 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 (2,0,-2,1).
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FORMULA
| a(n) = 5*n^2/4+((-1)^n-1)/8. - Omar E. Pol, Sep 28 2011
G.f.: x*(1+3*x+x^2)/(1-2*x+2*x^3-x^4). [Colin Barker, Jan 06 2012]
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EXAMPLE
| Contribution from Omar E. Pol, Sep 28 2011 (Start):
Illustration of initial terms (In a precise representation the pentagons should appear strictly concentric):
.
. o
. o o
. o o o o
. o o o o o o
. o o o o o o o o o
. o o o o o o o o o o
. o o o o o o o o o o o o o
. o o o o o o o o
. o o o o o o o o o o o o o o o
.
. 1 5 11 20 31
.
(End)
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MATHEMATICA
| Table[Round[5n^2/4], {n, 0, 39}] (* Alonso del Arte, Sep 28 2011 *)
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PROG
| (PARI) a(n)=5*n^2>>2 \\ Charles R Greathouse IV, Sep 28 2011
(MAGMA) [5*n^2/4+((-1)^n-1)/8: n in [0..50]]; // Vincenzo Librandi, Sep 29 2011
(Haskell)
a032527 n = a032527_list !! n
a032527_list = scanl (+) 0 a047209_list
-- Reinhard Zumkeller, Jan 07 2012
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CROSSREFS
| Cf. A000290, A032528, A077043, A195041. Column 5 of A195040. - Omar E. Pol, Sep 28 2011
Sequence in context: A190743 A110208 A034308 * A026038 A080957 A118375
Adjacent sequences: A032524 A032525 A032526 * A032528 A032529 A032530
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| New name from Omar E. Pol, Sep 28 2011
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