OFFSET
0,2
COMMENTS
An elephant sequence, see A175654. For the corner squares four A[5] vectors, with decimal values 58, 154, 178 and 184, lead to this sequence. For the central square these vectors lead to the companion sequence A033484. - Johannes W. Meijer, Aug 15 2010
a(n) is also the number of order-preserving partial isometries of an n-chain, i.e., the row sums of A183153 and A183154. - Abdullahi Umar, Dec 28 2010
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
F. Al-Kharousi, R. Kehinde and A. Umar, Combinatorial results for certain semigroups of partial isometries of a finite chain, The Australasian Journal of Combinatorics, Volume 58 (3) (2014), 363-375.
Index entries for linear recurrences with constant coefficients, signature (4,-5,2).
FORMULA
G.f.: (1 - 2*x + 3*x^2)/((1-x)^2*(1-2*x)).
a(n) = 2*a(n-1) + 2*n - 2, for n>0, with a(0)=1.
a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3).
From G. C. Greubel, Dec 30 2021: (Start)
a(n) = 2^n + 2*A000295(n).
E.g.f.: 3*exp(2*x) - 2*(1 + x)*exp(x). (End)
MATHEMATICA
Table[3 2^n-2n-2, {n, 0, 40}] (* or *) LinearRecurrence[{4, -5, 2}, {1, 2, 6}, 40] (* Harvey P. Dale, Oct 25 2011 *)
PROG
(PARI) a(n)=3*2^n-2*n-2 \\ Charles R Greathouse IV, Oct 07 2015
(Magma) [3*2^n -2*(n+1): n in [0..40]]; // G. C. Greubel, Dec 30 2021
(Sage) [3*2^n -2*(n+1) for n in (0..40)] # G. C. Greubel, Dec 30 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Aug 25 2004
STATUS
approved