A346006 Successive numbers arising from the Moessner construction of the sequence of fourth powers on page 64 of Conway-Guy's "Book of Numbers".

0, 1, 4, 6, 4, 16, 32, 24, 8, 81, 108, 54, 12, 256, 256, 96, 16, 625, 500, 150, 20, 1296, 864, 216, 24, 2401, 1372, 294, 28, 4096, 2048, 384, 32, 6561, 2916, 486, 36, 10000, 4000, 600, 40, 14641, 5324, 726, 44, 20736, 6912, 864, 48, 28561, 8788, 1014, 52, 38416, 10976, 1176, 56, 50625, 13500, 1350, 60

Offset: 0

Author

N. J. A. Sloane, Jul 25 2021

Keywords

• nonn

Comments

a(4*k+1) = (k+1)^2 for k >= 0.

References

• J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996. Sequence can be obtained by reading the successive circled numbers in the second display on page 64.

Crossrefs

Cf. A125714, A346004, A346005, A346595.

Programs

Maple

f:=proc(n,b) local i;
for i from 0 to b-1 do
if ((n+i) mod b) = 0 then return(binomial(b,i+1)*((n+i)/b)^(i+1)); fi;
od;
end;
[seq(f(n,3),n=0..60)];

Python

from sympy import binomial
def A346006(n):
    i = (4-n)%4
    return binomial(4,i+1)*((n+i)//4)**(i+1) # Chai Wah Wu, Jul 25 2021

Formula

Let b=4. If n == -i (mod b) for 0 <= i < b, then a(n) = binomial(b,i+1)*((n+i)/b)^(i+1).