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A258898 a(1)=a(2)=1, a(n) = ceiling(e*a(n-1) - a(n-2)) for n>2. 0
1, 1, 2, 5, 12, 28, 65, 149, 341, 778, 1774, 4045, 9222, 21023, 47925, 109251, 249051, 567740, 1294227, 2950334, 6725613, 15331778, 34950481, 79673480, 181624492, 414033077, 943834098, 2151574001, 4904750412, 11180919918 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Ratio of consecutive terms approaches A189040, (e + sqrt(e^2 - 4))/2.

LINKS

Table of n, a(n) for n=1..30.

EXAMPLE

a(2) = ceiling(e*1 - 1) = 2;

a(3) = ceiling(e*2 - 1) = 5;

a(4) = ceiling(e*5 - 2) = 12;

a(5) = ceiling(e*12 - 5) = 28.

MAPLE

a:= proc(n) option remember; `if`(n<3, 1,

      ceil(exp(1)*a(n-1)-a(n-2)))

    end:

seq(a(n), n=1..40);  # Alois P. Heinz, Jun 18 2015

MATHEMATICA

nxt[{a_, b_}]:={b, Ceiling[E*b-a]}; NestList[nxt, {1, 1}, 30][[All, 1]] (* Harvey P. Dale, Dec 02 2017 *)

PROG

(MAGMA) I:=[1, 1]; [n le 2 select I[n] else Ceiling(Exp(1)*Self(n-1)-Self(n-2)): n in [1..200]];

CROSSREFS

Cf. A001113, A189040.

Sequence in context: A045623 A290990 A001410 * A019486 A019485 A018914

Adjacent sequences:  A258895 A258896 A258897 * A258899 A258900 A258901

KEYWORD

nonn

AUTHOR

Morris Neene, Jun 14 2015

STATUS

approved

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Last modified October 17 14:22 EDT 2018. Contains 316281 sequences. (Running on oeis4.)