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 A047878 a(n) is the least number of knight's moves from corner (0,0) to n-th diagonal of unbounded chessboard. 3
 0, 3, 2, 1, 2, 3, 2, 3, 4, 3, 4, 5, 4, 5, 6, 5, 6, 7, 6, 7, 8, 7, 8, 9, 8, 9, 10, 9, 10, 11, 10, 11, 12, 11, 12, 13, 12, 13, 14, 13, 14, 15, 14, 15, 16, 15, 16, 17, 16, 17, 18, 17, 18, 19, 18, 19, 20, 19, 20, 21, 20, 21, 22, 21, 22, 23, 22, 23, 24, 23, 24, 25 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Apart from initial terms, same as A008611. - Anton Chupin, Oct 24 2009 LINKS G. C. Greubel, Table of n, a(n) for n = 0..5000 Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1). FORMULA a(n) = Min_{i=0..n} A049604(i,n-i). a(3n) = n, a(3n+1) = n+1, a(3n+2) = n+2 for n >= 1. From Colin Barker, May 04 2014: (Start) a(n) = a(n-1) + a(n-3) - a(n-4) for n>5. G.f.: x*(3-x-x^2-2*x^3+2*x^4) / ((1-x)^2*(1+x+x^2)). (End) From Guenther Schrack, Nov 19 2020: (Start) a(n) = a(n-3) + 1, for n > 4 with a(0) = 0, a(1) = 3, a(2) = 2, a(3) = 1, a(4) = 2; a(n) = (3*n + 6 - 2*(w^(2*n)*(2 + w) + w^n*(1 - w)))/9, for n > 1 with a(0) = 0, a(1) = 3, where w = (-1 + sqrt(-3))/2, a primitive third root of unity; a(n) = (n + 2 - 2*A057078(n))/3 for n > 1; a(n) = A194960(n-2) for n > 2; a(n) = (2*n + 2 - A330396(n))/3 for n > 1. (End) MATHEMATICA LinearRecurrence[{1, 0, 1, -1}, {0, 3, 2, 1, 2, 3}, 80] (* Harvey P. Dale, Sep 01 2018 *) Join[{0, 3}, Table[(n+2 -2*ChebyshevU[2*n, 1/2])/3, {n, 2, 75}]] (* G. C. Greubel, Oct 22 2022 *) PROG (PARI) concat(0, Vec(x*(2*x^4-2*x^3-x^2-x+3)/((x-1)^2*(x^2+x+1)) + O(x^100))) \\ Colin Barker, May 04 2014 (Magma) I:=[2, 1, 2, 3]; [0, 3] cat [n le 4 select I[n] else Self(n-1) +Self(n-3) -Self(n-4): n in [1..81]]; // G. C. Greubel, Oct 22 2022 (SageMath) (Sage) [0, 3]+[(n+2 - 2*chebyshev_U(2*n, 1/2))/3 for n in (2..75)] # G. C. Greubel, Oct 22 2022 CROSSREFS Cf. A008611, A049604, A057078, A194960, A330396. Sequence in context: A260450 A036583 A351557 * A324782 A256427 A120441 Adjacent sequences: A047875 A047876 A047877 * A047879 A047880 A047881 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified April 1 03:44 EDT 2023. Contains 361673 sequences. (Running on oeis4.)