The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 15 1999
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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