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 A051869 17-gonal (or heptadecagonal) numbers: a(n) = n*(15*n-13)/2. 15
 0, 1, 17, 48, 94, 155, 231, 322, 428, 549, 685, 836, 1002, 1183, 1379, 1590, 1816, 2057, 2313, 2584, 2870, 3171, 3487, 3818, 4164, 4525, 4901, 5292, 5698, 6119, 6555, 7006, 7472, 7953, 8449, 8960, 9486, 10027, 10583, 11154, 11740, 12341 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Sequence found by reading the line from 0, in the direction 0, 17,... and the parallel line from 1, in the direction 1, 48,..., in the square spiral whose vertices are the generalized 17-gonal numbers. - Omar E. Pol, Jul 18 2012 REFERENCES Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 189. E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 6. LINKS Ivan Panchenko, Table of n, a(n) for n = 0..1000 Index to sequences related to polygonal numbers Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA G.f.: x*(1+14*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011 a(n) = a(n-1) + 15*n - 14 with n>0, a(0)=0. - Vincenzo Librandi, Aug 06 2010 a(n) = A226489(n) - n. - Bruno Berselli, Jun 11 2013 a(15*a(n) + 106*n + 1) = a(15*a(n) + 106*n) + a(15*n+1). - Vladimir Shevelev, Jan 24 2014 E.g.f.: x*(2 + 15*x)*exp(x)/2. - G. C. Greubel, Aug 30 2019 Product_{n>=2} (1 - 1/a(n)) = 15/17. - Amiram Eldar, Jan 22 2021 MAPLE A051869 := proc(n) n*(15*n-13)/2 ; end proc: seq(A051869(n), n=0..30) ; # R. J. Mathar, Feb 05 2011 MATHEMATICA Table[n*(15*n - 13)/2, {n, 0, 40}] (* Robert Price, Oct 11 2018 *) PolygonalNumber[17, Range[0, 50]] (* Harvey P. Dale, Dec 14 2022 *) PROG (PARI) a(n)=n*(15*n-13)/2 \\ Charles R Greathouse IV, Jan 24 2014 (Magma) [n*(15*n-13)/2: n in [0..40]]; // G. C. Greubel, Aug 30 2019 (Sage) [n*(15*n-13)/2 for n in (0..40)] # G. C. Greubel, Aug 30 2019 (GAP) List([0..40], n-> n*(15*n-13)/2); # G. C. Greubel, Aug 30 2019 CROSSREFS Cf. A002378. Sequence in context: A362480 A159850 A031122 * A297818 A297988 A210372 Adjacent sequences: A051866 A051867 A051868 * A051870 A051871 A051872 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Dec 15 1999 STATUS approved

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Last modified June 14 21:35 EDT 2024. Contains 373401 sequences. (Running on oeis4.)