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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 (list; graph; refs; listen; history; text; internal format)
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) = (1/2) - (1/8)*sqrt(5)*{[9-4*sqrt(5)]^n - [9+4*sqrt(5)]^n} + (1/4)*{[9-4*sqrt(5)]^n + [9+4*sqrt(5)]^n}, with n>=0. - Paolo P. Lava, Nov 25 2008

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

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: A098345 A119043 A187204 * 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

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Last modified August 25 16:17 EDT 2019. Contains 326324 sequences. (Running on oeis4.)