A205539 Number of distinct values of Sum_{i=0..n} x(i)*binomial(n,i), where the x(i) have values in 0..4.

5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4089, 6705, 16327, 22689, 63573, 130389, 261393, 277569, 1029837, 993393, 3736239, 8378487, 16485497, 12937617, 49303463, 133933765, 258521683, 532893609, 1071289053, 666222975, 2514048099, 2149595937, 8785740659, 33471017703, 62738124385, 136742425621

Offset

0,1

Comments

Column 4 of A205542.

Links

Table of n, a(n) for n=0..35.

Maple

A205539:= proc(n)
   local bni, T, i;
   T:= {0};
   for i from 0 to n do
     bni:= binomial(n, i);
     T:= map(t -> (t, t+bni, t+2*bni, t+3*bni, t+4*bni), T)
   od:
   nops(T);
end;
seq(A205539(n), n=0..19); # Robert Israel, Jun 13 2014

Mathematica

a[n_] := a[n] = Module[{bni, T, i}, T = {0}; For[i = 0, i <= n, i++, bni = Binomial[n, i]; T = Union@ Flatten@ Map[{#, #+bni, #+2bni, #+3bni, #+4bni}&, T]]; Length[T]];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 24}] (* Jean-François Alcover, Jan 31 2023, after Robert Israel *)

Crossrefs

Cf. A205536, A205537, A205538, A205540, A205541, A205542.

Sequence in context: A258411 A059743 A000322 * A020737 A262452 A147401

Adjacent sequences: A205536 A205537 A205538 * A205540 A205541 A205542

Keyword

nonn

Author

R. H. Hardin, Jan 28 2012

Extensions

Typo in name corrected by Aaron Meyerowitz, Jun 13 2014

a(19)-a(24) from Robert Israel, Jun 13 2014

a(25)-a(35) from Bert Dobbelaere, Sep 15 2019

Status

approved