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A168198 a(n) = 3*n - a(n-1) + 1 with n > 1, a(1)=1. 2
1, 6, 4, 9, 7, 12, 10, 15, 13, 18, 16, 21, 19, 24, 22, 27, 25, 30, 28, 33, 31, 36, 34, 39, 37, 42, 40, 45, 43, 48, 46, 51, 49, 54, 52, 57, 55, 60, 58, 63, 61, 66, 64, 69, 67, 72, 70, 75, 73, 78, 76, 81, 79, 84, 82, 87, 85, 90, 88, 93, 91, 96, 94, 99, 97, 102, 100, 105, 103, 108 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Alternately add 5 and subtract 2, starting with 1. Apparently this was a test question: Find the next two numbers after 1,6,4,9,7,12,10. - N. J. A. Sloane, Dec 18 2010

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

D. Klein, What do the NAEP math tests really measure?, Notices Amer. Math. Soc., 58 (No. 1, 2011), 53-55.

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

FORMULA

a(n) = (6*n + 5 + 7*(-1)^n)/4. - Jon E. Schoenfield, Jun 24 2010

G.f.: x*(1+5*x-3*x^2)/((1+x)(1-x)^2). - Bruno Berselli, Feb 28 2012

EXAMPLE

From Muniru A Asiru, Mar 20 2018: (Start)

For n = 2, a(2) = 3*2 - a[2-1] + 1 = 6 - a[1] + 1 = 6 - 1 + 1 = 6.

For n = 3, a(3) = 3*3 - a[3-1] + 1 = 9 - a[2] + 1 = 9 - 6 + 1 = 4.

For n = 4, a(4) = 3*4 - a[4-1] + 1 = 12 - a[3] + 1 = 12 - 4 + 1 = 9.

... (End)

MAPLE

a:= proc(n) option remember: if n = 1 then 1 elif n >= 2 then 3*n - procname(n-1) + 1 fi; end:

seq(a(n), n = 1..70); # Muniru A Asiru, Mar 20 2018

MATHEMATICA

LinearRecurrence[{1, 1, -1}, {1, 6, 4}, 100] (* Vincenzo Librandi, Feb 28 2012 *)

PROG

(PARI) a(n)=(6*n+5+7*(-1)^n)/4 \\ Charles R Greathouse IV, Jan 11 2012

(MAGMA) I:=[1, 6, 4]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..60]]; // Vincenzo Librandi, Feb 28 2012

(GAP) a:=[1];; for n in [2..80] do a[n]:=3*n-a[n-1]+1; od; a; # Muniru A Asiru, Mar 20 2018

CROSSREFS

Cf. A084964, A103889, A168199, A168200.

Sequence in context: A086034 A191622 A021943 * A177898 A082209 A264770

Adjacent sequences:  A168195 A168196 A168197 * A168199 A168200 A168201

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Nov 20 2009

STATUS

approved

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Last modified October 14 08:54 EDT 2019. Contains 327995 sequences. (Running on oeis4.)