login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A137879 Numbers k such that k^2 is a 17-gonal number. 4
1, 133, 615, 64107, 296429, 30899441, 142878163, 14893466455, 68866978137, 7178619931869, 33193740583871, 3460079913694403, 15999314094447685, 1667751339780770377, 7711636199783200299, 803852685694417627311, 3716992648981408096433 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Corresponding 17-gonal numbers equal k^2 are listed in A137878.

The 17-gonal numbers A051869(n) = n(15n - 13)/2 are perfect squares for indices n listed in A137880. Note that all such indices are also perfect squares of numbers listed in A137881.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..745

Index entries for linear recurrences with constant coefficients, signature (0, 482, 0, -1).

FORMULA

a(n) = Sqrt[ A137878(n) ] = Sqrt[ A051869( A137880(n) ) ] = Sqrt[ A051869( A137881(n)^2 ) ].

For n>=5, a(n) = 482*a(n-2) - a(n-4). [Alekseyev]

a(2n) = (-60 + 17*sqrt(30))/120 * (11 + 2*sqrt(30))^(2n) + (-60 - 17*sqrt(30))/120 * (11 - 2*sqrt(30))^(2n). [Alekseyev]

a(2n+1) = (60 + 17*sqrt(30))/120 * (11 + 2*sqrt(30))^(2n) + (60 - 17*sqrt(30))/120 * (11 - 2*sqrt(30))^(2n). [Alekseyev]

MATHEMATICA

LinearRecurrence[{0, 482, 0, -1}, {1, 133, 615, 64107}, 20] (* Harvey P. Dale, May 12 2014 *)

PROG

(PARI) is(n)=ispolygonal(n^2, 17) \\ Charles R Greathouse IV, Oct 16 2015

CROSSREFS

Cf. A051869 (17-gonal numbers), A137878 (17-gonal numbers that are perfect squares), A137880, A137881.

Sequence in context: A251131 A267288 A334037 * A249108 A020237 A217690

Adjacent sequences:  A137876 A137877 A137878 * A137880 A137881 A137882

KEYWORD

nonn,easy

AUTHOR

Alexander Adamchuk, Feb 19 2008

EXTENSIONS

Edited and extended by Max Alekseyev, Oct 19 2008

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 13 06:22 EDT 2020. Contains 336442 sequences. (Running on oeis4.)