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A028375 Squares of (odd numbers not divisible by 5). 2
1, 9, 49, 81, 121, 169, 289, 361, 441, 529, 729, 841, 961, 1089, 1369, 1521, 1681, 1849, 2209, 2401, 2601, 2809, 3249, 3481, 3721, 3969, 4489, 4761, 5041, 5329, 5929, 6241, 6561, 6889, 7569, 7921, 8281, 8649, 9409, 9801, 10201, 10609, 11449, 11881, 12321 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Catalan stated empirically that the triple of any odd square not divisible by 5 is a sum of squares of three primes other than 2 and 3. - Jonathan Vos Post, Mar 03 2010  [Reference?]

LINKS

Rodolfo Ruiz-Huidobro, Table of n, a(n) for n = 1..250

Index entries for linear recurrences with constant coefficients, signature (1,0,0,2,-2,0,0,-1,1).

FORMULA

a(n) = (A045572(n))^2.

a(n) = a(n-1) + 2*a(n-4) - 2*a(n-5) - a(n-8) + a(n-9). - R. J. Mathar, Sep 22 2009

G.f.: x*(1 + 8*x + 40*x^2 + 32*x^3 + 38*x^4 + 32*x^5 + 40*x^6 + 8*x^7 + x^8)/((1 + x)^2 * (x^2 + 1)^2 * (1 - x)^3). - R. J. Mathar, Sep 22 2009

Sum_{n>=1} 1/a(n) = 3*Pi^2/25. - Amiram Eldar, Dec 19 2020

MATHEMATICA

Select[Range[1, 191, 2], Mod[#, 5] != 0 &]^2 (* or *) LinearRecurrence[{1, 0, 0, 2, -2, 0, 0, -1, 1}, {1, 9, 49, 81, 121, 169, 289, 361, 441}, 50] (* Harvey P. Dale, Feb 26 2017 *)

Complement[2Range[100] - 1, 5Range[20]]^2 (* Alonso del Arte, Dec 23 2019 *)

PROG

(Scala) ((1 to 99 by 2).diff(5 to 100 by 5)).map(n => (n * n)) // Alonso del Arte, Dec 23 2019

CROSSREFS

Sequence in context: A340239 A032589 A137175 * A167744 A032598 A352141

Adjacent sequences:  A028372 A028373 A028374 * A028376 A028377 A028378

KEYWORD

nonn,easy

AUTHOR

ems (nibor(AT)ix.netcom.com)

EXTENSIONS

Definition corrected by R. J. Mathar, Sep 22 2009

STATUS

approved

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Last modified July 2 15:50 EDT 2022. Contains 355029 sequences. (Running on oeis4.)