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A195145
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Concentric 14-gonal numbers.
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13
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0, 1, 14, 29, 56, 85, 126, 169, 224, 281, 350, 421, 504, 589, 686, 785, 896, 1009, 1134, 1261, 1400, 1541, 1694, 1849, 2016, 2185, 2366, 2549, 2744, 2941, 3150, 3361, 3584, 3809, 4046, 4285, 4536, 4789, 5054, 5321, 5600, 5881, 6174, 6469, 6776, 7085, 7406
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OFFSET
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0,3
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COMMENTS
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Also concentric tetradecagonal numbers or concentric tetrakaidecagonal numbers. Also sequence found by reading the line from 0, in the direction 0, 14,..., and the same line from 1, in the direction 1, 29,..., in the square spiral whose vertices are the generalized enneagonal numbers A118277. Main axis, perpendicular to A024966 in the same spiral.
Partial sums of A113801. [Reinhard Zumkeller, Jan 07 2012]
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LINKS
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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
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G.f. -x*(1+12*x+x^2) / ( (1+x)*(x-1)^3 ). - R. J. Mathar, Sep 18 2011
a(n) = (14*n^2+5*(-1)^n-5)/4; a(n) = a(-n) = -a(n-1)+7*n^2-7*n+1. - Vincenzo Librandi, Sep 27 2011
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PROG
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(MAGMA) [(14*n^2+5*(-1)^n-5)/4: n in [0..50]]; // Vincenzo Librandi, Sep 27 2011
(Haskell)
a195145 n = a195145_list !! n
a195145_list = scanl (+) 0 a113801_list
-- Reinhard Zumkeller, Jan 07 2012
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CROSSREFS
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Cf. A144555 and A195314 interleaved.
Cf. A032527, A032528, A077221, A195045, A195046, A195142, A195143, A195146, A195147, A195148, A195149.
Column 14 of A195040. - Omar E. Pol, Sep 28 2011
Sequence in context: A132756 A192836 A124681 * A041386 A041388 A042617
Adjacent sequences: A195142 A195143 A195144 * A195146 A195147 A195148
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KEYWORD
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nonn,easy
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AUTHOR
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Omar E. Pol, Sep 17 2011
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STATUS
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approved
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