This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
f := proc(n,k) option remember; if k > n then RETURN(0); fi; if k= 0 then if n=0 then RETURN(1) else RETURN(0); fi; fi; if n mod 2 = 1 then RETURN(f(n-1,k-1)); fi; f(n-1,k-1)+f(n/2,k); end; # present sequence is f(n,3)
a[n_] := If[n < 3, 0, ((1 - Mod[n, 2])*(1 - Mod[DigitCount[n, 2, 1], 2]) + 1)*If[Floor[(1/4)*DigitCount[n, 2, 1]] == 0, 1, 0]];
Table[a[n], {n, 0, 104}] (* Jean-François Alcover, Feb 13 2018, after Reinhard Zumkeller *)
h:= proc(n) option remember; `if`(n<1, 0,
`if`(n=2^ilog2(n), n, h(n-1)))
end:
b:= proc(n, i, k) option remember; `if`(n=0, `if`(k=0, 1, 0), `if`(
k>n or i*k b(n, h(n), 10):
seq(a(n), n=0..120);
T(6,3) = 4 because there are four ordered partitions of 6 into 3 powers of 2, namely: 4+1+1, 1+4+1, 1+1+4 and 2+2+2. Triangle begins: 1; 1, 1; 0, 2, 1; 1, 1, 3, 1; 0, 2, 3, 4, 1; 0, 2, 4, 6, 5, 1;
b:= proc(n) option remember; expand(`if`(n=0, 1,
add(b(n-2^j)*x, j=0..ilog2(n))))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=1..n))(b(n)):
seq(T(n), n=1..14); # Alois P. Heinz, Mar 06 2020
# Uses function PMatrix from A357368. Adds a row above and a column to the left.
PMatrix(10, n -> if n = 2^ilog2(n) then 1 else 0 fi); # Peter Luschny, Oct 07 2022
m:= 10; T[n_, k_]:= T[n, k]= Coefficient[(Sum[x^(2^j), {j,0,m+1}])^k, x, n]; Table[T[n, k], {n,10}, {k,n}]//Flatten (* G. C. Greubel, Mar 06 2020 *)
T[n_, k_] := T[n, k] = Which[k > n, 0, k == 0, If[n == 0, 1, 0], Mod[n, 2] == 1, T[n - 1, k - 1], True, T[n - 1, k - 1] + T[n/2, k]];
Table[T[n, k], {n, 1, 14}, {k, 1, n}] // Flatten (* Jean-François Alcover, Mar 07 2021 *)
Comments