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A195316
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Centered 36-gonal numbers.
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7
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1, 37, 109, 217, 361, 541, 757, 1009, 1297, 1621, 1981, 2377, 2809, 3277, 3781, 4321, 4897, 5509, 6157, 6841, 7561, 8317, 9109, 9937, 10801, 11701, 12637, 13609, 14617, 15661, 16741, 17857, 19009, 20197, 21421, 22681, 23977, 25309, 26677, 28081, 29521
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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, 37, ..., in the square spiral whose vertices are the generalized hendecagonal numbers A195160. Semi-axis opposite to A195321 in the same spiral.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..10000
John Elias, Illustration of initial terms.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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a(n) = 18*n^2 - 18*n + 1.
G.f.: -x*(1 + 34*x + x^2) / (x-1)^3. - R. J. Mathar, Sep 18 2011
Sum_{n>=1} 1/a(n) = Pi*tan(sqrt(7)*Pi/6)/(6*sqrt(7)). - Amiram Eldar, Feb 11 2022
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MATHEMATICA
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Table[18*n^2 - 18*n + 1, {n, 1, 40}] (* Amiram Eldar, Feb 11 2022 *)
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PROG
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(Magma) [(18*n^2-18*n+1): n in [1..50]]; // Vincenzo Librandi, Sep 19 2011
(PARI) a(n)=18*n^2-18*n+1 \\ Charles R Greathouse IV, Oct 07 2015
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CROSSREFS
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Bisection of A195147.
Cf. A003154, A069129, A069133, A069190, A195314, A195315, A195317, A195318.
Sequence in context: A171833 A257117 A033215 * A176549 A118536 A003164
Adjacent sequences: A195313 A195314 A195315 * A195317 A195318 A195319
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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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