A328886 Squares that end in 444.

1444, 213444, 289444, 925444, 1077444, 2137444, 2365444, 3849444, 4153444, 6061444, 6441444, 8773444, 9229444, 11985444, 12517444, 15697444, 16305444, 19909444, 20593444, 24621444, 25381444, 29833444, 30669444, 35545444, 36457444, 41757444, 42745444, 48469444

Offset

1,1

Comments

See A039685 for further information about these numbers.

References

Albert H. Beiler, Recreations in the Theory of Numbers (2nd ed.), 1966, p. 139.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..400

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

Formula

a(n) = A039685(n)^2.

From Elmo R. Oliveira, Apr 09 2026: (Start)

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).

G.f.: 4*x*(361 + 53000*x + 18278*x^2 + 53000*x^3 + 361*x^4)/((x + 1)^2*(1 - x)^3). (End)

Mathematica

Select[Table[n*10^3+444, {n, 50000}], IntegerQ[Sqrt[#]]&] (* Harvey P. Dale, Jun 19 2020 *)
Flatten[Table[500n+{38, -38}, {n, 0, 20}]]^2//Union (* Harvey P. Dale, Jan 26 2025 *)

Prog

(PARI) a039685(n) = 250*n+87*(-1)^n-125
a(n) = a039685(n)^2

Crossrefs

Cf. A039685.

Sequence in context: A298222 A374267 A180465 * A031754 A031536 A181973

Adjacent sequences: A328883 A328884 A328885 * A328887 A328888 A328889

Keyword

nonn,base,easy

Author

Felix Fröhlich, Oct 29 2019

Status

approved