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

1,3

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).

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A006451, A006452.

Sequence in context: A164607 A200189 A240383 * A202296 A299530 A238982

Adjacent sequences: A160967 A160968 A160969 * A160971 A160972 A160973

Keyword

nonn,easy

Author

Sture Sjöstedt, Jun 01 2009, Jul 02 2009

Extensions

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

Status

approved