A143100 A007318 * A143098.

1, 3, 4, 6, 13, 30, 64, 129, 256, 510, 1021, 2046, 4096, 8193, 16384, 32766, 65533, 131070, 262144, 524289, 1048576, 2097150, 4194301, 8388606, 16777216, 33554433, 67108864, 134217726, 268435453, 536870910, 1073741824, 2147483649, 4294967296, 8589934590

Offset: 1

Author

Gary W. Adamson, Jul 24 2008

Keywords

• nonn

Examples

			a(4) = 6 = (1, 3, 3, 1) dot (1, 2, -1, 2) = (1 + 6 - 3 + 2).
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A143097, A143098, A143099.

Programs

Maple

A143098 := proc(n) if(n=1)then return 1: elif(n mod 3 = 0)then return -1: else return 2: fi: end: A143100 := proc(n) return add(binomial(n-1,k-1)*A143098(k),k=1..n): end: seq(A143100(n),n=1..34); # Nathaniel Johnston, Apr 30 2011

Formula

Binomial transform of A143098: (1, 2, -1, 2, 2, -1, 2, 2, -1, 2, 2, ...).

From R. J. Mathar, Jul 31 2008: (Start)

G.f.: (3x^3 - 2x^2 - x + 1)*x/((x^2-x+1)*(2x-1)*(x-1)).

a(n) = -1 + 2^(n-1) + A057079(n-1). (End)