A110213 a(n+3) = 6*a(n) - 5*a(n+2), a(0) = 1, a(1) = -7, a(2) = 35.
1, -7, 35, -169, 803, -3805, 18011, -85237, 403355, -1908709, 9032123, -42740485, 202250171, -957058117, 4528847675, -21430737349, 101411338043, -479883604165, 2270833596731, -10745699955397, 50849198151995, -240620989179589, 1138630746165563, -5388058541915845
Offset: 0
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (-5,0,6).
Programs
-
Maple
seriestolist(series((-1+2*x)/((x-1)*(6*x^2+6*x+1)), x=0,25)); -or- Floretion Algebra Multiplication Program, FAMP Code: 2baseksumseq[A*B] with A = + 'i + 'ii' + 'ij' + 'ik' and B = + .5'i - .5'j + .5'k + .5i' + .5j' - .5k' - .5'ij' - .5'ik' + .5'ji' + .5'ki' Sumtype is set to: sum[(Y[0], Y[1], Y[2]),mod(3)
-
Mathematica
LinearRecurrence[{-5,0,6},{1,-7,35},30] (* Harvey P. Dale, Mar 01 2015 *)
Formula
G.f. (-1+2*x)/((x-1)*(6*x^2+6*x+1))
a(x)=(3-Sqrt[3]+(7-8*Sqrt[3])(-3+Sqrt[3])^x+(-3-Sqrt[3])^x (-10+9*Sqrt[3]))/(13*(-3+Sqrt[3])). - Harvey P. Dale, Mar 01 2015