A137880 Indices k of perfect squares among 17-gonal numbers A051869(k) = k*(15*k - 13)/2.

1, 49, 225, 23409, 108241, 11282881, 52171729, 5438325025, 25146664929, 2621261378961, 12120640323841, 1263442546333969, 5842123489426225, 608976686071593889, 2815891401263116401, 293525499243961920321, 1357253813285332678849, 141478681658903574000625

Offset: 1

Author

Alexander Adamchuk, Feb 19 2008

Keywords

• nonn
• easy

Comments

Corresponding perfect squares are listed in A137878.

Note that all a(n) are perfect squares themselves, their square roots are listed in A137881.

Links

• Matthew House, Table of n, a(n) for n = 1..746
• Index entries for linear recurrences with constant coefficients, signature (1,482,-482,-1,1).

Crossrefs

Cf. A051869 (17-gonal numbers), A137878 (17-gonal numbers that are perfect squares), A137879, A137881.

Programs

Mathematica

Rest@ CoefficientList[Series[x (1 + 48 x - 306 x^2 + 48 x^3 + x^4)/((1 - x) (1 - 22 x + x^2) (1 + 22 x + x^2)), {x, 0, 18}], x] (* Michael De Vlieger, Jun 18 2016 *)

PARI

Vec(x*(1+48*x-306*x^2+48*x^3+x^4)/((1-x)*(1-22*x+x^2)*(1+22*x+x^2)) + O(x^20)) \\ Colin Barker, Jun 18 2016

Formula

A051869( a(n) ) = A137878(n); a(n) = A137881(n)^2.

From Max Alekseyev, Oct 19 2008: (Start)

a(n) = 482*a(n-2) - a(n-4) - 208.

a(2n) = ( (15 - sqrt(30))/30 * (11 + 2*sqrt(30))^n + (15 + sqrt(30))/30 * (11 - 2*sqrt(30))^n )^2.

a(2n+1) = ( (15 + sqrt(30))/30 * (11 + 2*sqrt(30))^n + (15 - sqrt(30))/30 * (11 - 2*sqrt(30))^n )^2. (End)

a(n) = a(n-1) + 482*a(n-2) - 482*a(n-3) - a(n-4) + a(n-5). - Matthew House, Jun 18 2016

G.f.: x*(1 + 48*x - 306*x^2 + 48*x^3 + x^4) / ((1-x)*(1 - 22*x + x^2)*(1 + 22*x + x^2)). - Colin Barker, Jun 18 2016

Extensions

Edited and extended by Max Alekseyev, Oct 19 2008