A346005 Successive numbers arising from the Moessner construction of the cubes on page 64 of Conway-Guy's "Book of Numbers".

0, 1, 3, 3, 8, 12, 6, 27, 27, 9, 64, 48, 12, 125, 75, 15, 216, 108, 18, 343, 147, 21, 512, 192, 24, 729, 243, 27, 1000, 300, 30, 1331, 363, 33, 1728, 432, 36, 2197, 507, 39, 2744, 588, 42, 3375, 675, 45, 4096, 768, 48, 4913, 867, 51, 5832, 972, 54, 6859, 1083, 57, 8000, 1200

Offset

0,3

References

J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996. Sequence can be seen in the successive circled numbers at the top of page 64.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (0,0,4,0,0,-6,0,0,4,0,0,-1).

Formula

a(n) = n if n mod 3 = 0, = ((n+2)/3)^3 if n mod 3 = 1, and otherwise (n+1)^2/3.

G.f.: x*(1 + 3*x + 3*x^2 + 4*x^3 - 6*x^5 + x^6 - 3*x^7 + 3*x^8)/((1 - x)^4*(1 + x + x^2)^4). - Andrew Howroyd, Nov 12 2025

Maple

f:=proc(n) if (n mod 3) = 0 then n
elif (n mod 3) = 1 then ((n+2)/3)^3;
else (n+1)^2/3; fi; end;
[seq(f(n), n=0..100)];

Mathematica

A346005[n_] := Switch[Mod[n, 3], 0, n, 1, ((n + 2)/3)^3, _, (n + 1)^2/3];
Array[A346005, 60, 0] (* Paolo Xausa, Nov 13 2025 *)

Prog

(Python)
def A346005(n): return n if n % 3 == 0 else ((n+2)//3)**3 if n % 3 == 1 else (n+1)**2//3 # Chai Wah Wu, Jul 25 2021
(PARI) a(n) = { my(r=n%3); if (r == 0, n, if(r==1, ((n+2)/3)^3, (n+1)^2/3)) } \\ Andrew Howroyd, Nov 12 2025

Crossrefs

Cf. A125714, A346004, A346006-A346007, A346595.

Sequence in context: A105039 A358834 A384330 * A276552 A213030 A364468

Adjacent sequences: A346002 A346003 A346004 * A346006 A346007 A346008

Keyword

nonn,easy

Author

N. J. A. Sloane, Jul 25 2021

Status

approved