A159780 Inner product of the binary representation of n and its reverse.

0, 1, 0, 2, 0, 2, 1, 3, 0, 2, 0, 2, 0, 2, 2, 4, 0, 2, 0, 2, 1, 3, 1, 3, 0, 2, 2, 4, 1, 3, 3, 5, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 4, 2, 4, 0, 2, 2, 4, 0, 2, 2, 4, 0, 2, 2, 4, 2, 4, 4, 6, 0, 2, 0, 2, 0, 2, 0, 2, 1, 3, 1, 3, 1, 3, 1, 3, 0, 2, 0, 2, 2, 4, 2, 4, 1, 3, 1, 3, 3, 5, 3, 5, 0, 2, 2, 4, 0, 2, 2, 4, 1

Offset

0,4

Comments

a(n) gives the number of 1's that coincide in the binary representation of n and its reverse. For the n in A140900, we have a(n)=0. The number k first appears at n=2^k-1.

Also central terms and right edge of the triangle in A173920: a(n)=A173920(2*n,n)=A173920(n,n). [From Reinhard Zumkeller, Mar 04 2010]

a(A000225(n)) = n and a(m) < n for m < A000225(n). [Reinhard Zumkeller, Oct 21 2011]

a(n) = sum(A030308(n,k)*A030308(n,A070939(n)-1-k): k = 0..A070939(n)-1). - Reinhard Zumkeller, Mar 10 2013

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Example

14 is represented by the binary vector (1,1,1,0). The reverse is (0,1,1,1). The inner product is 1*0+1*1+1*1+0*1 = 2. Hence a(14) = 2.

Mathematica

Table[d=IntegerDigits[n, 2]; d.Reverse[d], {n, 0, 1023}]

Prog

(Haskell)
a159780 n = sum $ zipWith (*) bs $ reverse bs
   where bs = a030308_row n
-- Reinhard Zumkeller, Mar 10 2013, Oct 21 2011

Crossrefs

Cf. A216176.

Sequence in context: A291440 A061986 A127185 * A355739 A324285 A138036

Adjacent sequences: A159777 A159778 A159779 * A159781 A159782 A159783

Keyword

nonn,base

Author

T. D. Noe, Apr 22 2009

Status

approved