A061981 a(n) = 3^n - 2*n - 1.
0, 0, 4, 20, 72, 232, 716, 2172, 6544, 19664, 59028, 177124, 531416, 1594296, 4782940, 14348876, 43046688, 129140128, 387420452, 1162261428, 3486784360, 10460353160, 31381059564, 94143178780, 282429536432, 847288609392
Offset: 0
Links
- Harry J. Smith, Table of n, a(n) for n = 0..200
- Brandon Alberts and Jack Klys, The distribution of H8-extensions of quadratic fields, arXiv:1611.05595 [math.NT], 2016. See p. 17.
- Index entries for linear recurrences with constant coefficients, signature (5,-7,3).
Programs
-
Mathematica
Table[3^n-2n-1,{n,0,30}] (* or *) LinearRecurrence[{5,-7,3},{0,0,4},30] (* Harvey P. Dale, Mar 30 2018 *) -
PARI
a(n) = { 3^n - 2*n - 1 } \\ Harry J. Smith, Jul 29 2009 -
SageMath
[3^n -(2*n+1) for n in (0..40)] # G. C. Greubel, Jun 13 2022
Formula
From Bruno Berselli, Jan 31 2012: (Start)
G.f.: 4*x^2/((1-3*x)*(1-x)^2).
a(n) = A186948(n) - 1.
a(n+2) = 4*A000340(n). (End)
From Deisy J. Camacho, Feb 26 2021 (Start)
a(n) = Sum_{j=2..n} Sum_{i=0..j} n!/((j-i)!*i!*(n-j)!).
a(n) = 4 + 4*a(n-1) - 3*a(n-2). (End)
E.g.f.: exp(3*x) - (2*x + 1)*exp(x). - G. C. Greubel, Jun 13 2022