A137879 Numbers k such that k^2 is a 17-gonal number.

1, 133, 615, 64107, 296429, 30899441, 142878163, 14893466455, 68866978137, 7178619931869, 33193740583871, 3460079913694403, 15999314094447685, 1667751339780770377, 7711636199783200299, 803852685694417627311, 3716992648981408096433

Offset: 1

Author

Alexander Adamchuk, Feb 19 2008

Keywords

• nonn
• easy

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).

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

a(n) = sqrt(A137878(n)) = sqrt(A051869(A137880(n))) = sqrt(A051869(A137881(n)^2)).

From Max Alekseyev, Oct 19 2008: (Start)

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

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

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

Extensions

Extended by Max Alekseyev, Oct 19 2008