A160970 Indices of square numbers that are also 18-gonal numbers.

0, 1, 10, 44, 341, 1495, 11584, 50786, 393515, 1725229, 13367926, 58607000, 454115969, 1990912771, 15426575020, 67632427214, 524049434711, 2297511612505, 17802254205154, 78047762397956, 604752593540525, 2651326409917999, 20543785926172696, 90067050174814010

Offset: 1

Author

Sture Sjöstedt, Jun 01 2009, Jul 02 2009

Keywords

• nonn
• easy

Comments

Solving the Diophantine equation A051870(m) = m*(8*m-7) = k^2 leads to the entries.

k in the sequence and a list of associated m = 0, 1, 4, 16, 121, 529, 4096, 17956, 139129, 609961...

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,34,0,-1).

Crossrefs

Cf. A006451, A006452.

Programs

Mathematica

Join[{0},LinearRecurrence[{0,34,0,-1},{1,10,44,340},23]] (* Ray Chandler, Aug 01 2015 *)

PARI

is(n)=ispolygonal(n^2,18) \\ Charles R Greathouse IV, Feb 14 2013

PARI

concat(0, Vec(x^2*(x+1)*(x^2+9*x+1)/((x^2-6*x+1)*(x^2+6*x+1)) + O(x^50))) \\ Colin Barker, Jun 24 2015

Formula

a(n) = 34*a(n-2) - a(n-4), n>5. - R. J. Mathar, Oct 04 2009

G.f.: x^2*(x+1)*(x^2 + 9*x + 1)/((x^2 - 6*x + 1)*(x^2 + 6*x + 1)). - Colin Barker, Oct 07 2012

For all values excepting the leading 0, a(n) = sqrt(8*A006452(n)^2 - 7)*A006452(n) = sqrt(A006451(n-1)*(A006451(n-1) + 1)/2 + 1)*(2*A006451(n-1) + 1). - Raphie Frank, Feb 11 2013

Extensions

0 added in front and extended by R. J. Mathar, Oct 04 2009