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A160970 Indices of square numbers that are also 18-gonal numbers. 1
0, 1, 10, 44, 341, 1495, 11584, 50786, 393515, 1725229, 13367926, 58607000, 454115969, 1990912771, 15426575020, 67632427214, 524049434711, 2297511612505, 17802254205154, 78047762397956, 604752593540525, 2651326409917999, 20543785926172696, 90067050174814010 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 6 22:42 EST 2021. Contains 349567 sequences. (Running on oeis4.)