A052276 Nonnegative numbers of the form n^3 (+/-) 3, n >= 0.

3, 4, 5, 11, 24, 30, 61, 67, 122, 128, 213, 219, 340, 346, 509, 515, 726, 732, 997, 1003, 1328, 1334, 1725, 1731, 2194, 2200, 2741, 2747, 3372, 3378, 4093, 4099, 4910, 4916, 5829, 5835, 6856, 6862, 7997, 8003, 9258, 9264, 10645, 10651

Offset

1,1

Comments

It is conjectured that A003325 and A052276 (the current sequence) have infinitely many numbers in common, although only one example (128) is known.

The next such example must be larger than 2*10^12. - M. F. Hasler, Jan 10 2021

Another term common to A003325 and A052276 can be derived from the equality 569936821221962380720^3 + (-569936821113563493509)^3 + (-472715493453327032)^3 = 3 (Booker and Sutherland, see Links). - Giovanni Resta, Sep 09 2025

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Andrew R. Booker and Andrew V. Sutherland, On a question of Mordell, arXiv:2007.01209 [math.NT], 2021.

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

Formula

a(n) = a(n-1)+3*a(n-2)-3*a(n-3)-3*a(n-4)+3*a(n-5)+a(n-6)-a(n-7) for n>8. - Colin Barker, Jul 09 2015

G.f.: x*(5*x^7-8*x^6-9*x^5+19*x^4+3*x^3-8*x^2+x+3) / ((x-1)^4*(x+1)^3). - Colin Barker, Jul 09 2015

a(n) = ((2*n+1)*(n^2+n+1) - (-1)^n*(3*n^2+3*n-47))/16 for n >= 2. - Robert Israel, Jul 09 2015

a(n) = ceiling(n/2)^3 + 3*(-1)^n for all n > 1. - M. F. Hasler, Jan 10 2021

Maple

3, 4, op(map(n -> (n^3-3, n^3+3), [$2..100])); # Robert Israel, Jul 09 2015

Prog

(PARI) Vec(x*(5*x^7-8*x^6-9*x^5+19*x^4+3*x^3-8*x^2+x+3)/((x-1)^4*(x+1)^3) + O(x^100)) \\ Colin Barker, Jul 09 2015
(PARI) apply( {A052276(n)=(n\/2)^3+3*(-1)^n+(n==1)*5}, [1..99]) \\ M. F. Hasler, Jan 10 2021
(Python)
def A052276(n): return (n+1>>1)**3+(-3 if n&1 else 3) if n>1 else 3 # Chai Wah Wu, Jun 27 2025

Crossrefs

Sequence in context: A318077 A074221 A341785 * A173096 A385022 A378395

Adjacent sequences: A052273 A052274 A052275 * A052277 A052278 A052279

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 05 2000

Status

approved