A144472 Negative values along the main diagonal of the array defined by A020806 and its differences.

-1, 2, 9, 13, 31, 57, 119, 233, 471, 937, 1879, 3753, 7511, 15017, 30039, 60073, 120151, 240297, 480599, 961193, 1922391, 3844777, 7689559, 15379113, 30758231, 61516457, 123032919, 246065833, 492131671, 984263337, 1968526679, 3937053353, 7874106711

Offset: 1

Author

Paul Curtz, Oct 10 2008, Oct 14 2008

Keywords

• sign
• easy

Examples

			A020806 and its repeated differences in the next rows start as follows:
..1,..4,..2,..8,..5,..7,..1,..4,..2,..8, <- A020806
..3,.-2,..6,.-3,..2,.-6,..3,.-2,..6,.-3, <- A131969
.-5,..8,.-9,..5,.-8,..9,.-5,..8,.-9,..5,
.13,-17,.14,-13,.17,-14,.13,-17,.14,-13,
-30,.31,-27,.30,-31,.27,-30,.31,-27,.30,
.61,-58,.57,-61,.58,-57,.61,-58,.57,-61,
The diagonal is 1,-2,-9,-13,-31,... which yields a(n) after signs are flipped.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,2).

Programs

Mathematica

Join[{-1}, LinearRecurrence[{1, 2}, {2, 9}, 40]] (* Jean-François Alcover, Nov 06 2017 *)

PARI

Vec(-x*(1 - 3*x - 9*x^2) / ((1 + x)*(1 - 2*x)) + O(x^50)) \\ Colin Barker, Nov 06 2017

Formula

a(n+1) - 2*a(n) = (-1)^n*A010716(n), n>1, period 2.

G.f.: x*(1-3*x-9*x^2) / ((1+x)*(2*x-1)). - R. J. Mathar, Oct 24 2008

a(n) = 11*2^(n-2)/3 - 5*(-1)^n/3, n>1. - R. J. Mathar, Oct 24 2008

From Colin Barker, Nov 06 2017: (Start)

a(n) = (11*2^n - 20) / 12 for n>1 and even.

a(n) = (11*2^n + 20) / 12 for n>1 and odd.

a(n) = a(n-1) + 2*a(n-2) for n>3.

(End)

Extensions

Edited and extended by R. J. Mathar, Oct 24 2008