A346006 - OEIS

%I #21 Jul 27 2021 06:22:51

%S 0,1,4,6,4,16,32,24,8,81,108,54,12,256,256,96,16,625,500,150,20,1296,

%T 864,216,24,2401,1372,294,28,4096,2048,384,32,6561,2916,486,36,10000,

%U 4000,600,40,14641,5324,726,44,20736,6912,864,48,28561,8788,1014,52,38416,10976,1176,56,50625,13500,1350,60

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

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

%D 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.

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

%p f:=proc(n,b) local i;

%p for i from 0 to b-1 do

%p if ((n+i) mod b) = 0 then return(binomial(b,i+1)*((n+i)/b)^(i+1)); fi;

%p od;

%p end;

%p [seq(f(n,3),n=0..60)];

%o (Python)

%o from sympy import binomial

%o def A346006(n):

%o     i = (4-n)%4

%o     return binomial(4,i+1)*((n+i)//4)**(i+1) # _Chai Wah Wu_, Jul 25 2021

%Y Cf. A125714, A346004, A346005, A346595.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Jul 25 2021