A088560 - OEIS

%I #20 Apr 18 2020 00:07:36

%S 1,2,2,8,2,12,32,128,2,20,92,464,992,4032,8192,32768,2,36,308,2320,

%T 9692,52712,164320,781312,1470944,6249152,13748672,56768768,67100672,

%U 268419072,536870912,2147483648,2,68,1124,14352,117812,1003960,5670400

%N Sum of odd entries in row n of Pascal's triangle.

%C a(n) = a power of 2 iff n = 2^k - 2, 2^k - 1 or 2^k.

%C a(n) = A088504(n) iff n = 2^k - 2, k>1. a(n) > A088504(n) iff n = 2^k - 1.

%C Sums of rows of the triangle in A143333. - _Reinhard Zumkeller_, Oct 24 2010

%H Robert Israel, <a href="/A088560/b088560.txt">Table of n, a(n) for n = 0..3420</a>

%F a(n) + A088504(n) = 2^n. A088504(n) - a(n) = A085814(n).

%F a(2^n)=2; a(2^n-1)=2^(2^n-1); a(2^n+1)=2^(n+1)+4 ... - _Benoit Cloitre_, Nov 19 2003

%p T:= [1]: R:= 1:

%p for i from 1 to 50 do

%p   T:= [1,op(T[2..-1]+T[1..-2]),1];

%p   R:= R, convert(select(type,T,odd),`+`)

%p od:

%p R; # _Robert Israel_, Apr 17 2020

%t f[n_] := Plus @@ Select[ Table[ Binomial[n, i], {i, 0, n}], OddQ[ # ] & ]; Table[ f[n], {n, 0, 38}] (* _Robert G. Wilson v_, Nov 19 2003 *)

%o (PARI) a(n)=sum(i=0,n,binomial(n,i)*(binomial(n,i)%2))

%Y Cf. A001316, A088504, A085814, A143333.

%K nonn,look

%O 0,2

%A Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 17 2003

%E Edited and extended by _Robert G. Wilson v_ and _Ray Chandler_, Nov 19 2003