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 A195316 Centered 36-gonal numbers. 7
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS 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). FORMULA 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 MATHEMATICA Table[18*n^2 - 18*n + 1, {n, 1, 40}] (* Amiram Eldar, Feb 11 2022 *) PROG (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 CROSSREFS 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 KEYWORD nonn,easy AUTHOR Omar E. Pol, Sep 16 2011 STATUS approved

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Last modified May 25 09:45 EDT 2022. Contains 354066 sequences. (Running on oeis4.)