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

0,1

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

Table of n, a(n) for n=0..43.

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

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

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 *)

Prog

(Magma) [2*n^2+36*n+227: n in [0..50]] /* or */ 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
(PARI) a(n)=2*n^2+36*n+227 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A259058.

Sequence in context: A031513 A078765 A179141 * A333425 A142261 A117458

Adjacent sequences: A259056 A259057 A259058 * A259060 A259061 A259062

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 12 2015

Status

approved