A180046 a(n+1) = a(n-3) + a(n-2) - a(n-1) + a(n) starting with 1, 2, 3, 4.

1, 2, 3, 4, 4, 5, 8, 11, 12, 14, 21, 30, 35, 40, 56, 81, 100, 115, 152, 218, 281, 330, 419, 588, 780, 941, 1168, 1595, 2148, 2662, 3277, 4358, 5891, 7472, 9216, 11993, 16140, 20835, 25904, 33202, 44273, 57810, 72643, 92308, 121748, 159893, 203096, 257259

Offset: 1

Author

Ian Stewart, Aug 08 2010

Keywords

• nonn
• easy

Examples

			1 2 3 4 (by definition); 1 + 2 - 3 + 4 = 4, 2 + 3 - 4 + 4 = 5, 3 + 4 - 4 + 5 = 8.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,-1,1,1).

Crossrefs

Cf. A100329.

Programs

Haskell

import Data.List (zipWith4)
a180046 n = a180046_list !! (n-1)
a180046_list = [1..4] ++ zipWith4 (((((+) .) . (+)) .) . (-))
                          (drop 3 a180046_list) (drop 2 a180046_list)
                            (tail a180046_list) a180046_list
-- Reinhard Zumkeller, Oct 08 2014

Mathematica

LinearRecurrence[{1,-1,1,1},{1,2,3,4},50] (* Harvey P. Dale, Mar 18 2015 *)

PARI

Vec(x*(1+x)*(2*x^2+1)/(1-x+x^2-x^3-x^4)+O(x^99)) \\ Charles R Greathouse IV, Jul 06 2011

Formula

G.f.: -x*(1+x)*(2*x^2+1)/(-1+x-x^2+x^3+x^4). - R. J. Mathar, Aug 14 2010

a(n) = (-1)^(n)*(A100329(n-1)-A100329(n)-2*A100329(n-2)+2*A100329(n-3)) with A100329(-1) = A100329(-2) = 0. - Johannes W. Meijer, Jul 06 2011

Extensions

More terms from R. J. Mathar, Aug 14 2010

Name edited by Michel Marcus, Feb 20 2025