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

%I A346006 #21 Jul 27 2021 06:22:51
%S A346006 0,1,4,6,4,16,32,24,8,81,108,54,12,256,256,96,16,625,500,150,20,1296,
%T A346006 864,216,24,2401,1372,294,28,4096,2048,384,32,6561,2916,486,36,10000,
%U A346006 4000,600,40,14641,5324,726,44,20736,6912,864,48,28561,8788,1014,52,38416,10976,1176,56,50625,13500,1350,60
%N A346006 Successive numbers arising from the Moessner construction of the sequence of fourth powers on page 64 of Conway-Guy's "Book of Numbers".
%C A346006 a(4*k+1) = (k+1)^2 for k >= 0.
%D A346006 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 A346006 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 A346006 f:=proc(n,b) local i;
%p A346006 for i from 0 to b-1 do
%p A346006 if ((n+i) mod b) = 0 then return(binomial(b,i+1)*((n+i)/b)^(i+1)); fi;
%p A346006 od;
%p A346006 end;
%p A346006 [seq(f(n,3),n=0..60)];
%o A346006 (Python)
%o A346006 from sympy import binomial
%o A346006 def A346006(n):
%o A346006     i = (4-n)%4
%o A346006     return binomial(4,i+1)*((n+i)//4)**(i+1) # _Chai Wah Wu_, Jul 25 2021
%Y A346006 Cf. A125714, A346004, A346005, A346595.
%K A346006 nonn
%O A346006 0,3
%A A346006 _N. J. A. Sloane_, Jul 25 2021