A259059 One half of numbers representable in at least two different ways as sums of four distinct nonvanishing squares. See A259058 for these numbers and their representations.

227, 265, 307, 353, 403, 457, 515, 577, 643, 713, 787, 865, 947, 1033, 1123, 1217, 1315, 1417, 1523, 1633, 1747, 1865, 1987, 2113, 2243, 2377, 2515, 2657, 2803, 2953, 3107, 3265, 3427, 3593, 3763, 3937, 4115, 4297, 4483, 4673, 4867, 5065, 5267, 5473

Offset: 0

Author

Wolfdieter Lang, Aug 12 2015

Keywords

• nonn
• easy

Comments

There may be other numbers with this property.

References

• W. Sierpiński, 250 Problems in Elementary Number Theory, American Elsevier Publ. Comp., New York, PWN-Polish Scientific Publishers, Warszawa, 1970, Problem 227, p. 20 and p. 110.

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A259058.

Programs

Magma

[2*n^2+36*n+227: n in [0..50]]; // Vincenzo Librandi, Aug 13 2015

Magma

I:=[227, 265, 307]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Aug 13 2015

Maple

A259059:=n->2*n^2 + 36*n + 227: seq(A259059(n), n=0..50); # Wesley Ivan Hurt, Aug 13 2015

Mathematica

CoefficientList[Series[(227 - 416 x + 193 x^2)/(1 - x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Aug 13 2015 *)

PARI

a(n)=2*n^2+36*n+227 \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = A259058(n)/2.

a(n) = 2*n^2 + 36*n + 227.

O.g.f.: (227 - 416*x + 193*x^2)/(1-x)^3.

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). - Vincenzo Librandi, Aug 13 2015