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A088560 Sum of odd entries in row n of Pascal's triangle.

%I A088560 #20 Apr 18 2020 00:07:36
%S A088560 1,2,2,8,2,12,32,128,2,20,92,464,992,4032,8192,32768,2,36,308,2320,
%T A088560 9692,52712,164320,781312,1470944,6249152,13748672,56768768,67100672,
%U A088560 268419072,536870912,2147483648,2,68,1124,14352,117812,1003960,5670400
%N A088560 Sum of odd entries in row n of Pascal's triangle.
%C A088560 a(n) = a power of 2 iff n = 2^k - 2, 2^k - 1 or 2^k.
%C A088560 a(n) = A088504(n) iff n = 2^k - 2, k>1. a(n) > A088504(n) iff n = 2^k - 1.
%C A088560 Sums of rows of the triangle in A143333. - _Reinhard Zumkeller_, Oct 24 2010
%H A088560 Robert Israel, <a href="/A088560/b088560.txt">Table of n, a(n) for n = 0..3420</a>
%F A088560 a(n) + A088504(n) = 2^n. A088504(n) - a(n) = A085814(n).
%F A088560 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 A088560 T:= [1]: R:= 1:
%p A088560 for i from 1 to 50 do
%p A088560   T:= [1,op(T[2..-1]+T[1..-2]),1];
%p A088560   R:= R, convert(select(type,T,odd),`+`)
%p A088560 od:
%p A088560 R; # _Robert Israel_, Apr 17 2020
%t A088560 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 A088560 (PARI) a(n)=sum(i=0,n,binomial(n,i)*(binomial(n,i)%2))
%Y A088560 Cf. A001316, A088504, A085814, A143333.
%K A088560 nonn,look
%O A088560 0,2
%A A088560 Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 17 2003
%E A088560 Edited and extended by _Robert G. Wilson v_ and _Ray Chandler_, Nov 19 2003