A137878 Perfect squares among 17-gonal numbers A051869(k) = k*(15*k - 13)/2.

1, 17689, 378225, 4109707449, 87870152041, 954775454112481, 20414169462254569, 221815343046210267025, 4742660677722035990769, 51532584126226886201833161, 1101824413949324675985344641, 11972153009151467313136073526409, 255978051492792346696545201859225

Offset: 1

Author

Alexander Adamchuk, Feb 19 2008

Keywords

• nonn
• easy

Comments

Corresponding square roots sqrt(a(n)) are listed in A137879.

Indices of perfect squares among the 17-gonal numbers A051869(k) = k*(15*k - 13)/2 are listed in A137880. Note that all such indices are also perfect squares, their square roots are listed in A137881(k) = sqrt(A137880(k)).

Links

• Colin Barker, Table of n, a(n) for n = 1..350
• Index entries for linear recurrences with constant coefficients, signature (1,232322,-232322,-1,1).

Crossrefs

Cf. A051869 (17-gonal numbers), A137879, A137880, A137881.

Programs

PARI

Vec(x*(1+17688*x+128214*x^2+17688*x^3+x^4)/((1-x)*(1-482*x+x^2)*(1+482*x+x^2)) + O(x^20)) \\ Colin Barker, Jun 19 2016

Formula

a(n) = A137879(n)^2 = A051869( A137880(n) ) = A051869( A137881(n)^2 ).

From Colin Barker, Jun 19 2016: (Start)

a(n) = a(n-1) + 232322*a(n-2) - 232322*a(n-3) - a(n-4) + a(n-5) for n > 5.

G.f.: x*(1 + 17688*x + 128214*x^2 + 17688*x^3 + x^4) / ((1-x)*(1 - 482*x + x^2)*(1 + 482*x + x^2)).

(End)

Extensions

Edited and extended by Max Alekseyev, Oct 19 2008