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A133273
Indices of centered decagonal numbers which are also decagonal numbers.
3
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
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
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. A128922.
Sequence in context: A119043 A187204 A346458 * A239763 A112703 A132676
KEYWORD
nonn,easy
AUTHOR
Richard Choulet, Oct 16 2007
EXTENSIONS
More terms from Paolo P. Lava, Nov 25 2008
STATUS
approved