A182453 a(n) = 3^n - n*(n-1)/2.

1, 3, 8, 24, 75, 233, 714, 2166, 6533, 19647, 59004, 177092, 531375, 1594245, 4782878, 14348802, 43046601, 129140027, 387420336, 1162261296, 3486784211, 10460352993, 31381059378, 94143178574, 282429536205, 847288609143, 2541865828004, 7625597484636, 22876792454583, 68630377364477, 205891132094214, 617673396283482, 1853020188851345, 5559060566554995

Offset

0,2

Comments

For n>0, r(n)=a(n)/a(n-1) is approximately equal to 3. Average of the sum of r(n) is 3. Except for r(3) = 2.666666666666667, all other r(n)'s are just above zero and r(n) tends to 3 as n tends to infinity.

Links

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (6,-12,10,-3).

Formula

G.f.: (1-3*x+2*x^2+2*x^3)/((1-x)^3*(1-3*x)). - Colin Barker, May 07 2012

Example

For n=6, a(n)=714, a(n-1)=233, r(n)=3.0643776824034334763948497854077.
For n=21, a(n)=10460352993, a(n-1)=3486784211, r(n) = 3.0000001032469972946083183924341.

Crossrefs

Sequence in context: A281872 A046342 A238977 * A047087 A000958 A148782

Adjacent sequences: A182450 A182451 A182452 * A182454 A182455 A182456

Keyword

nonn,easy

Author

Aditya Subramanian, Apr 29 2012

Extensions

Edited by N. J. A. Sloane, May 01 2012

Status

approved