[seqfan] Re: id: A132045
franktaw at netscape.net
franktaw at netscape.net
Sat Jan 17 21:03:39 CET 2009
This formula is off by one. Note that the offset of A132045 is 0, not
1. Thus the correct formula is
a(n) = 2^n - n + 1 = A000325(n) + 1,
which holds for n >= 1.
I have submitted a correction.
Franklin T. Adams-Watters
-----Original Message-----
From: avik roy <avik_3.1416 at yahoo.co.in>
I've suggested a general formula for generating terms in A132045, it is
given by
a(n+1)=2^n-n+1; n>=1
the proof is given here:
It is easy to observe, the rows of A132044 are simply produced by
keeping the
1st and last 1's untouched in Pascal's triangle and by reducing the
intermediate
terms by 1.
Thus the sum of (n+1)th rows is given by,
1 + [C(n,1) + C(n,2) + C(n,3) + ... + C(n-1)] - (n-1) + 1
= 2+2^n-2-n+1=2^n-n+1
More information about the SeqFan
mailing list