A261241 One half of numbers representable in at least two different ways as sums of four nonvanishing cubes. See A259060 for these numbers and their representations.

3213, 3950, 4807, 5796, 6929, 8218, 9675, 11312, 13141, 15174, 17423, 19900, 22617, 25586, 28819, 32328, 36125, 40222, 44631, 49364, 54433, 59850, 65627, 71776, 78309, 85238, 92575, 100332, 108521, 117154, 126243, 135800, 145837, 156366

Offset

0,1

Comments

See A259060. 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..33.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = (n+9)*(2*n^2 + 36*n + 357), n >= 0.

O.g.f.: (3213 - 8902*x + 8285*x^2 - 2584*x^3)/(1-x)^4.

a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Vincenzo Librandi, Aug 13 2015

Mathematica

CoefficientList[Series[(3213 - 8902 x + 8285 x^2 - 2584 x^3)/(1 - x)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Aug 13 2015 *)

Prog

(Magma) [(n+9)*(2*n^2 + 36*n + 357): n in [0..50]] /* or */ I:=[3213, 3950, 4807, 5796]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Aug 13 2015

Crossrefs

Cf. A259060.

Sequence in context: A048255 A303995 A091329 * A345772 A020414 A202612

Adjacent sequences: A261238 A261239 A261240 * A261242 A261243 A261244

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 12 2015

Status

approved