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A033570
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Pentagonal numbers with odd index: (2*n+1)*(3*n+1).
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9
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1, 12, 35, 70, 117, 176, 247, 330, 425, 532, 651, 782, 925, 1080, 1247, 1426, 1617, 1820, 2035, 2262, 2501, 2752, 3015, 3290, 3577, 3876, 4187, 4510, 4845, 5192, 5551, 5922, 6305, 6700, 7107, 7526, 7957, 8400, 8855, 9322, 9801, 10292, 10795, 11310, 11837
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| If Y is a 3-subset of an 2n-set X then, for n>=4, a(n-2) is the number of 4-subsets of X having at least two elements in common with Y. - Milan R. Janjic (agnus(AT)blic.net), Dec 16 2007
Sequence found by reading the line (one of the diagonal axes) from 1, in the direction 1, 12,..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. - Omar E. Pol, Sep 08 2011
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| G.f.: A(x) = (1+9*x+2*x^2)/(1-x)^3.
a(n)=a(n-1)+12*n-1 (with a(0)=1) [From Vincenzo Librandi, Nov 17 2010]
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {1, 12, 35}, 45]
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CROSSREFS
| Cf. A000326, A049452, A033568.
Cf. A001318, A049453. - Omar E. Pol, Sep 08 2011
Sequence in context: A088596 A077293 A053682 * A163661 A142074 A102085
Adjacent sequences: A033567 A033568 A033569 * A033571 A033572 A033573
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Ray Chandler (rayjchandler(AT)sbcglobal.net), Dec 08 2011
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