A140139 Binomial transform of [1, 1, 2, -3, 4, -5, 6, -7, ...].

1, 2, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141

Offset: 1

Author

Gary W. Adamson, May 09 2008

Keywords

• nonn
• easy

Comments

Apart from initial term, identical to A130773 if offsets are ignored. - R. J. Mathar, May 11 2008

Examples

			a(4) = 7 = (1, 3, 3, 1) dot (1, 1, 2, -3) = (1 + 3 + 6 - 3).
		

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A007318, A130773.

Programs

Mathematica

LinearRecurrence[{2,-1},{1,2,5,7},71] (* Stefano Spezia, Apr 20 2025 *)

Formula

Equals A007318 * [1, 1, 2, -3, 4, -5, 6, -7, ...].

Sums of antidiagonal terms of the following array: 1, 1, 1, 1, 1, ... 1, 3, 5, 7, 9, ... 1, 1, 1, 1, 1, ...

O.g.f.: x*(1 + 2*x^2 - x^3)/(1 - x)^2. - R. J. Mathar, May 11 2008

E.g.f.: 1 - x^2/2 - exp(x)*(1 - 2*x). - Stefano Spezia, Apr 20 2025