A133273 Indices of centered decagonal numbers which are also decagonal numbers.

1, 10, 171, 3060, 54901, 985150, 17677791, 317215080, 5692193641, 102142270450, 1832868674451, 32889493869660, 590178020979421, 10590314883759910, 190035489886698951, 3410048503076821200, 61190837565496082641, 1098025027675852666330, 19703259660599851911291

Offset

1,2

Comments

Numbers k such that 80*k^2 - 80*k + 25 is a square.

Also the indices of centered square numbers which are also centered pentagonal numbers. - Colin Barker, Jan 01 2015

Links

Colin Barker, Table of n, a(n) for n = 1..798

Index entries for linear recurrences with constant coefficients, signature (19,-19,1).

Formula

a(n+2) = 18*a(n+1) - a(n) - 8.

a(n+1) = 9*a(n) - 4 + sqrt(80*a(n)^2 - 80*a(n) + 25).

G.f.: x*(-1+9*x)/(-1+x)/(1 - 18*x + x^2). - R. J. Mathar, Nov 14 2007

a(n) = 19*a(n-1) - 19*a(n-2) + a(n-3). - Colin Barker, Jan 01 2015

Product_{n>=2} (1 - 1/a(n)) = 2/sqrt(5) (= A010532 / 10). - Amiram Eldar, Dec 02 2024

Mathematica

LinearRecurrence[{19, -19, 1}, {1, 10, 171}, 20] (* Harvey P. Dale, Oct 09 2020 *)

Prog

(PARI) Vec(x*(-1+9*x)/((-1+x)*(1-18*x+x^2)) + O(x^100)) \\ Colin Barker, Jan 01 2015

Crossrefs

Cf. A001107, A001844, A005891, A010532, A062786, A128922.

Sequence in context: A119043 A187204 A346458 * A239763 A112703 A132676

Adjacent sequences: A133270 A133271 A133272 * A133274 A133275 A133276

Keyword

nonn,easy

Author

Richard Choulet, Oct 16 2007

Extensions

More terms from Paolo P. Lava, Nov 25 2008

Status

approved