A166122 a(n) = (7-(-5)^n)/6.

1, 2, -3, 22, -103, 522, -2603, 13022, -65103, 325522, -1627603, 8138022, -40690103, 203450522, -1017252603, 5086263022, -25431315103, 127156575522, -635782877603, 3178914388022, -15894571940103, 79472859700522

Offset: 0

Author

Philippe Deléham, Oct 07 2009

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-4,5).

Crossrefs

Cf. A084222, A084247, A166114.

Programs

Mathematica

LinearRecurrence[{-4,5},{1,2},30] (* Harvey P. Dale, Mar 10 2016 *)
Table[(7 - (-5)^n)/6, {n, 24}] (* or *)
CoefficientList[Series[(1 + 6 x)/(1 + 4 x - 5 x^2), {x, 0, 24}], x] (* Michael De Vlieger, Apr 27 2016 *)

Formula

a(n) = 5*a(n-2) - 4*a(n-1), a(0)= 1, a(1)= 2, for n>1.

a(n) = 7-5*a(n-1), a(0)=1.

a(n) = a(n-1)+(-5)^(n-1), a(0)=1.

O.g.f.: (1+6*x)/(1+4*x-5*x^2).

E.g.f.: (7*exp(x)-exp(-5*x))/6.