A239322 Interleave (-1)^n*(A000182(n+1) - A000364(n)), -A028296(n+1).

0, 1, 1, -5, -11, 61, 211, -1385, -6551, 50521, 303271, -2702765, -19665491, 199360981, 1704396331, -19391512145, -190473830831, 2404879675441, 26684005437391, -370371188237525

Offset: 0

Author

Paul Curtz, Mar 28 2014

Keywords

• sign

Comments

Difference table of a(n):

0, 1, 1, -5, -11, 61, 211, -1385,...

1, 0, -6, -6, 72, 150, -1596,...

-1, -6, 0, 78, 78, -1746,...

-5, -6, 78, 0, -1824,...

11, 72, 78, -1824,...

61, -150, -1746,...

-211, -1596,...

-1385,...

etc.

a(n) is an autosequence (its inverse binomial transform is the signed sequence) of the first kind (its main diagonal is A000004=0's and the first two upper diagonal are the same). Like A000045(n).

Note that e(n) = A000111(n+1) - A000111(n) = 0, 0, 1, 3, 11, 45, 211,... is not in the OEIS. a(2n) = (-1)*(n+1)*e(2n).

Antidiagonals upon A000004:

1,

1,

-6, -5,

-6, -11,

78, 72, 61,

78, 150, 211,

Row sum: 1, 1, -11, -17, 211, 439,... .

b(n) = a(n) mod 9 = 0 followed by period 6: repeat 1, 1, 4, 7, 7, 4 is also an autosequence of the first kind.

Examples

			a(0)=1-1=0, a(1)=-(-1)=1, a(2)=2-1=1, a(3)=-5, a(4)=-(16-5)=-11.
		

Crossrefs

Cf. Zig (A000364) and Zag (A000182) give Euler A000111(n).