A105580 a(n+3) = a(n) - a(n+1) - a(n+2); a(0) = -5, a(1) = 6, a(2) = 0.

-5, 6, 0, -11, 17, -6, -22, 45, -29, -38, 112, -103, -47, 262, -318, 9, 571, -898, 336, 1133, -2367, 1570, 1930, -5867, 5507, 2290, -13664, 16881, -927, -29618, 47426, -18735, -58309, 124470, -84896, -97883, 307249, -294262, -110870, 712381, -895773, 72522, 1535632, -2503927, 1040817, 2998742

Offset: 0

Author

Creighton Dement, Apr 14 2005

Keywords

• sign
• easy

Comments

Floretion Algebra Multiplication Program, FAMP Code: 2tesforseq[.5'j + .5'k + .5j' + .5k' + .5'ii' + .5e], 1vesforseq = A000004, ForType: 1A.

Examples

			This sequence was generated using the same floretion which generated the sequences A105577, A105578, A105579, etc.. However, in this case a force transform was applied. [Specifically, (a(n)) may be seen as the result of a tesfor-transform of the zero-sequence A000004 with respect to the floretion given in the program code.]
		

Links

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

Crossrefs

Cf. A002249, A014551, A078020, A105577, A105578, A105581.

Programs

Mathematica

Transpose[NestList[Join[Rest[#],ListCorrelate[ {1,-1,-1}, #]]&,{-5,6,0},50]][[1]]  (* Harvey P. Dale, Mar 14 2011 *)
CoefficientList[Series[(5-x-x^2)/(x^3-x^2-x-1),{x,0,50}],x]  (* Harvey P. Dale, Mar 14 2011 *)

Formula

G.f. (5-x-x^2)/(x^3-x^2-x-1)

a(n) = A078046(n-1) - A073145(n+3).

a(n) = -5*A057597(n+2) + A057597(n+1)+A057597(n). - R. J. Mathar, Oct 25 2022