A028375 Squares of (odd numbers not divisible by 5).

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, 12769

Offset

1,2

Comments

Catalan stated empirically: The triple of any odd square not divisible by 5 is the sum of squares concerning three primes, excluding 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.

From R. J. Mathar, Sep 22 2009: (Start)

a(n) = a(n-1) + 2*a(n-4) - 2*a(n-5) - a(n-8) + a(n-9).

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). (End)

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 (* Harvey P. Dale, Feb 26 2017 *)
(* Alternative: *)
LinearRecurrence[{1, 0, 0, 2, -2, 0, 0, -1, 1}, {1, 9, 49, 81, 121, 169, 289, 361, 441}, 46] (* Harvey P. Dale, Feb 26 2017 *)
(* Alternative: *)
Complement[2Range[100] - 1, 5Range[40]]^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
(PARI) for(n=0, 56, my(k=2*n+1); if(!(k%5==0), print1(k^2", "))) \\ Bruce Nye, May 11 2026
(PARI) apply(sqr, select(x->(gcd(x, 10)==1), [1..150])) \\ Michel Marcus, May 11 2026

Crossrefs

Sequence in context: A032589 A137175 A167744 * A383487 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