

A165754


a(n) = nimsum(n+(n+1)+(n+2)).


1



3, 0, 5, 2, 7, 4, 9, 6, 11, 8, 13, 10, 15, 12, 17, 14, 19, 16, 21, 18, 23, 20, 25, 22, 27, 24, 29, 26, 31, 28, 33, 30, 35, 32, 37, 34, 39, 36, 41, 38, 43, 40, 45, 42, 47, 44, 49, 46, 51, 48, 53, 50, 55, 52, 57, 54, 59, 56, 61, 58, 63, 60, 65, 62, 67, 64, 69, 66, 71, 68, 73, 70
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OFFSET

0,1


COMMENTS

Start with 3. Then repeat the cycle: subtract 3, add 5. The oddindexed terms give the odd numbers, beginning with 3. The evenindexed terms give the even numbers, beginning with 0. In the infinite sequence, every positive integer except 1 is listed.


LINKS

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,1).


FORMULA

a(n) = 2*na(n1)+1 (with a(0)=3).  Vincenzo Librandi, Dec 02 2010
a(n) = 1 + n + 2*(1)^n.  R. J. Mathar, Dec 02 2010
From Colin Barker, Nov 05 2015: (Start)
a(n) = a(n1) + a(n2)  a(n3) for n>2.
G.f.: (2*x^23*x+3) / ((x1)^2*(x+1)).
(End)


EXAMPLE

For n = 3, Nimsum(3 + 4 + 5) = 2, as shown: 011 XOR 100 XOR 101 010.


MAPLE

read("transforms") ; A165754 := proc(n) nimsum(nimsum(n, n+1), n+2) ; end: seq(A165754(n), n=0..120) ; # R. J. Mathar, Sep 28 2009


MATHEMATICA

Flatten[NestList[{Last[#]+5, Last[#]+2}&, {3, 0}, 40]] (* Harvey P. Dale, Dec 04 2011 *)


PROG

(Python) while n < 100 . . . print n^(n+1)^(n+2) . . . n=n+1
(PARI) Vec((2*x^23*x+3)/((x1)^2*(x+1)) + O(x^100)) \\ Colin Barker, Nov 05 2015


CROSSREFS

Cf. A065168.  R. J. Mathar, Sep 28 2009
Sequence in context: A159980 A098496 A175297 * A193067 A177886 A011293
Adjacent sequences: A165751 A165752 A165753 * A165755 A165756 A165757


KEYWORD

nonn,easy


AUTHOR

Mick Purcell (mickpurcell(AT)gmail.com), Sep 26 2009


EXTENSIONS

Extended by R. J. Mathar, Sep 28 2009


STATUS

approved



