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 A004444 Nimsum n + 3. 4
 3, 2, 1, 0, 7, 6, 5, 4, 11, 10, 9, 8, 15, 14, 13, 12, 19, 18, 17, 16, 23, 22, 21, 20, 27, 26, 25, 24, 31, 30, 29, 28, 35, 34, 33, 32, 39, 38, 37, 36, 43, 42, 41, 40, 47, 46, 45, 44, 51, 50, 49, 48, 55, 54, 53, 52, 59, 58 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The same as A120634 except for first 3 terms. - Pietro Battiston, Jan 19 2008 Permutation of the nonnegative integers. - Wesley Ivan Hurt, Apr 06 2016 REFERENCES E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 60. J. H. Conway, On Numbers and Games. Academic Press, NY, 1976, pp. 51-53. LINKS Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1). FORMULA G.f.: (4*x^4-x^3-x^2-x+3)/((x-1)^2*(x+1)*(x^2+1)). - Ralf Stephan, Nov 01 2003 a(n) = n + (-1)^n + 2*(-1)^floor(n/2). - Mitchell Harris, Jan 10 2005 From Wesley Ivan Hurt, Apr 06 2016: (Start) a(n) = a(n-1) + a(n-4) - a(n-5) for n>4. a(n) = n + (-1)^n + 2*(-1)^((2*n-1+(-1)^n)/4). a(n) = A004442(A004443(n)) = A004443(A004442(n)). a(a(n)) = n; n+a(n) = A004442(n) + A004443(n). (End) MAPLE A004444:=n->n+(-1)^n+2*(-1)^floor(n/2): seq(A004444(n), n=0..50); # Wesley Ivan Hurt, Apr 06 2016 MATHEMATICA CoefficientList[Series[(4x^4-x^3-x^2-x+3)/((x-1)^2(x+1) (x^2+1)), {x, 0, 70}], x] (* Harvey P. Dale, Mar 24 2011 *) Table[n + (-1)^n + 2 (-1)^Floor[n/2], {n, 0, 100}] (* Wesley Ivan Hurt, Apr 06 2016 *) PROG (MAGMA) [n + (-1)^n + 2*(-1)^Floor(n/2): n in [0..100]]; // Wesley Ivan Hurt, Apr 06 2016 (PARI) Vec((4*x^4-x^3-x^2-x+3)/((x-1)^2*(x+1)*(x^2+1)) + O(x^90)) \\ Michel Marcus, Apr 06 2016 CROSSREFS Cf. A004442 (nimsum n+1), A004443 (nimsum n+2), A120634. Sequence in context: A098825 A111460 A035327 * A204533 A259790 A246654 Adjacent sequences:  A004441 A004442 A004443 * A004445 A004446 A004447 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified December 14 01:41 EST 2019. Contains 329978 sequences. (Running on oeis4.)