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A097813 a(n) = 3*2^n - 2*n - 2. 6
1, 2, 6, 16, 38, 84, 178, 368, 750, 1516, 3050, 6120, 12262, 24548, 49122, 98272, 196574, 393180, 786394, 1572824, 3145686, 6291412, 12582866, 25165776, 50331598, 100663244, 201326538, 402653128, 805306310, 1610612676, 3221225410, 6442450880, 12884901822, 25769803708 (list; graph; refs; listen; history; text; internal format)
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, 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 - 2x + 3x^2)/((1-x)^2(1-2x)).

a(n) = 2a(n-1) + 2n-2, n>0, a(0)=1.

a(n) = 4a(n-1) - 5a(n-2) + 2a(n-3).

MATHEMATICA

s=2; lst={1, s}; Do[s+=(s+=n); AppendTo[lst, s], {n, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 11 2008 *)

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

CROSSREFS

Cf. A079583.

Sequence in context: A099099 A074082 A212383 * A167821 A093041 A156616

Adjacent sequences:  A097810 A097811 A097812 * A097814 A097815 A097816

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Aug 25 2004

EXTENSIONS

Alternative description, additional reference and crossrefs

STATUS

approved

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Last modified April 23 22:17 EDT 2019. Contains 322388 sequences. (Running on oeis4.)