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A179805 a(0) = 1, a(1) = 3, a(2) = 6; a(n), n>2 = 2*a(n-1) - a(n-2). a(n), n>2 = a(n-1) + 9. 2
1, 3, 6, 15, 24, 33, 42, 51, 60, 69, 78, 87, 96, 105, 114, 123, 132, 141, 150, 159, 168, 177, 186, 195, 204, 213, 222, 231, 240, 249, 258, 267, 276, 285, 294, 303, 312, 321, 330, 339, 348, 357, 366, 375, 384, 393, 402 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

For n> 1, a(n) == 6 mod 9.

Apart from the second term, the same as A122709. [From R. J. Mathar, Jul 30 2010]

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,-1).

FORMULA

(1 + 3x + 6x^2 + 15x^3 + ...) = (1 + 3x^2 + 3x^3 + 3x^4 + ...) *

(1 + 3x + 3x^2 + 3x^3 + 3x^4 + ...).

a(0) = 1, a(1) = 3, a(2) = 6; a(n), n>2 = 2*a(n-1) - a(n-2).

a(n), n>2 = a(n-1) + 9.

a(n) = 9*n-12 for n>1. G.f.: (2*x+1)*(3*x^2-x+1)/(x-1)^2. [Colin Barker, Oct 28 2012]

EXAMPLE

a(4) = 24 = 9 + a(3) = 9 + 15.

a(4) = 24 = 2*a(3) - a(2) = 2*15 - 6.

MATHEMATICA

LinearRecurrence[{2, -1}, {1, 3, 6, 15}, 50] (* Harvey P. Dale, Sep 25 2018 *)

CROSSREFS

Sequence in context: A129602 A298015 A044888 * A006639 A242757 A166448

Adjacent sequences:  A179802 A179803 A179804 * A179806 A179807 A179808

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Jul 27 2010

STATUS

approved

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Last modified December 15 22:02 EST 2019. Contains 330012 sequences. (Running on oeis4.)