A085814 -id:A085814 - cp's OEIS frontend

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

1, 2, 2, 8, 2, 12, 32, 128, 2, 20, 92, 464, 992, 4032, 8192, 32768, 2, 36, 308, 2320, 9692, 52712, 164320, 781312, 1470944, 6249152, 13748672, 56768768, 67100672, 268419072, 536870912, 2147483648, 2, 68, 1124, 14352, 117812, 1003960, 5670400

Offset: 0

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

a(n) = a power of 2 iff n = 2^k - 2, 2^k - 1 or 2^k.
a(n) = A088504(n) iff n = 2^k - 2, k>1. a(n) > A088504(n) iff n = 2^k - 1.
Sums of rows of the triangle in A143333. - Reinhard Zumkeller, Oct 24 2010

Robert Israel, Table of n, a(n) for n = 0..3420

Cf. A001316, A088504, A085814, A143333.

T:= [1]: R:= 1:
for i from 1 to 50 do
  T:= [1,op(T[2..-1]+T[1..-2]),1];
  R:= R, convert(select(type,T,odd),`+`)
od:
R; # Robert Israel, Apr 17 2020

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 *)

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

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

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

Edited and extended by Robert G. Wilson v and Ray Chandler, Nov 19 2003

A088504 Sum of even entries in row n of Pascal's triangle.

Original entry on oeis.org

0, 0, 2, 0, 14, 20, 32, 0, 254, 492, 932, 1584, 3104, 4160, 8192, 0, 65534, 131036, 261836, 521968, 1038884, 2044440, 4029984, 7607296, 15306272, 27305280, 53360192, 77448960, 201334784, 268451840, 536870912, 0, 4294967294

Offset: 0

Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 18 2003

nonn

a(n) = 0 iff n = 2^k - 1.

A088560(n) = A088504(n) iff n = 2^k - 2, k>1. A088560(n) > A088504(n) iff n = 2^k - 1.

Cf. A048967.

f[n_] := Plus @@ Select[ Table[ Binomial[n, i], {i, 0, n}], EvenQ[ # ] & ]; Table[ f[n], {n, 0, 35}] (* Robert G. Wilson v, Nov 19 2003 *)

A088504(n) + A088560(n) = 2^n. A088504(n) - A088560(n) = A085814(n).

Edited and extended by Robert G. Wilson v and Ray Chandler, Nov 19 2003

cp's OEIS Frontend

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

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