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

1,2

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).

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A192359 A100453 A017150 * A264538 A266799 A211741

Adjacent sequences: A137877 A137878 A137879 * A137881 A137882 A137883

Keyword

nonn,easy

Author

Alexander Adamchuk, Feb 19 2008

Extensions

Edited and extended by Max Alekseyev, Oct 19 2008

Status

approved