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A195314
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Centered 28-gonal numbers.
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6
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1, 29, 85, 169, 281, 421, 589, 785, 1009, 1261, 1541, 1849, 2185, 2549, 2941, 3361, 3809, 4285, 4789, 5321, 5881, 6469, 7085, 7729, 8401, 9101, 9829, 10585, 11369, 12181, 13021, 13889, 14785, 15709, 16661, 17641, 18649, 19685, 20749, 21841, 22961, 24109
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OFFSET
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1,2
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COMMENTS
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Sequence found by reading the line from 1, in the direction 1, 29, ..., in the square spiral whose vertices are the generalized enneagonal numbers A118277. Semi-axis opposite to A144555 in the same spiral.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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a(n) = 14*n^2 - 14*n + 1.
G.f.: -x*(1 + 26*x + x^2) / (x-1)^3. - R. J. Mathar, Sep 18 2011
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Oct 01 2011
Sum_{n>=1} 1/a(n) = Pi*tan(sqrt(5/7)*Pi/2)/(2*sqrt(35)). - Amiram Eldar, Feb 11 2022
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MATHEMATICA
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Table[14n^2-14n+1, {n, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 29, 85}, 50]
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PROG
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(Magma) [(14*n^2-14*n+1): n in [1..50]]; // Vincenzo Librandi, Sep 19 2011
(PARI) a(n)=14*n^2-14*n+1 \\ Charles R Greathouse IV, Oct 07 2015
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CROSSREFS
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Bisection of A195145.
Cf. A003154, A069129, A069133, A069190, A195315, A195316, A195317, A195318.
Sequence in context: A343683 A255187 A273362 * A323218 A124784 A126383
Adjacent sequences: A195311 A195312 A195313 * A195315 A195316 A195317
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KEYWORD
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nonn,easy
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AUTHOR
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Omar E. Pol, Sep 16 2011
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STATUS
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approved
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