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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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 * A142261 A117458 A252026

Adjacent sequences:  A259056 A259057 A259058 * A259060 A259061 A259062

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Aug 12 2015

STATUS

approved

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Last modified November 21 09:14 EST 2019. Contains 329362 sequences. (Running on oeis4.)