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A158464 Number of distinct squares in row n of Pascal's triangle. 1
1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
It seems that some subset of terms in A055997 (A115599) gives the positions of 3's. E.g., we have a(9) = a(50) = a(289) = a(9801) = 3, but on the other hand, a(1682) = a(57122) = 2. - Antti Karttunen, Nov 03 2017
LINKS
FORMULA
a(n) = Sum_{k=0..floor(n/2)} A010052(A007318(n,k));
a(A000290(n)) > 1 for n > 1.
EXAMPLE
a(8) = #{1} = 1;
a(9) = #{1,9,36} = 3.
MAPLE
A158464 := proc(n)
local sqset, k ;
sqset := {} ;
for k from 0 to n do
P := binomial(n, k) ;
if issqr(P) then
sqset := sqset union {P} ;
end if;
end do:
nops(sqset) ;
end proc:
seq(A158464(n), n=0..120) ; # R. J. Mathar, Jul 09 2016
MATHEMATICA
CountDistinct /@ Table[Sqrt@ Binomial[n, k] /. k_ /; ! IntegerQ@ k -> Nothing, {n, 0, 104}, {k, 0, n}] (* Michael De Vlieger, Nov 03 2017 *)
PROG
(PARI) A158464(n) = sum(k=0, n\2, issquare(binomial(n, k))); \\ Antti Karttunen, Nov 03 2017
CROSSREFS
Sequence in context: A154950 A260089 A296240 * A056926 A137773 A175010
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Mar 19 2009
EXTENSIONS
More terms from Antti Karttunen, Nov 03 2017
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)