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 A357946 a(n) is the number in the infinite multiplication table that the chess knight reaches in n moves, starting from the number 1, the angle between adjacent segments being 90 degrees alternately changing direction to the left and to the right. 1
 1, 6, 8, 20, 21, 40, 40, 66, 65, 98, 96, 136, 133, 180, 176, 230, 225, 286, 280, 348, 341, 416, 408, 490, 481, 570, 560, 656, 645, 748, 736, 846, 833, 950, 936, 1060, 1045, 1176, 1160, 1298, 1281, 1426, 1408, 1560, 1541, 1700, 1680, 1846, 1825, 1998, 1976 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The route of the chess knight is an endless zigzag broken line starting from (1,1) and taking steps alternately (+1,+2) and (+2,-1). Successive steps are 90-degree turns left and right. The even-indexed terms are the positive octagonal numbers (cf. A000567) and are lined up in a straight line. LINKS Table of n, a(n) for n=0..50. Nicolay Avilov, Drawing with the beginning of the route, Nicolay Avilov, Problem 2403. Sequence in the Pythagorean table (in Russian). Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1). FORMULA a(n) = (3*n^2 + 8*n + 4)/4 if n is an even number, a(n) = (3*n^2 + 16*n + 5)/4 if n is an odd number. a(n) = (6*n + 3 + (-1)^n)*(2*n + 7 - 3*(-1)^n)/16, where n is any natural number. a(n) = A001651(n+1)*A052938(n). EXAMPLE The route of the chess knight (1,1)-(2,3)-(4,2)-(5,4)-(7,3)-(8,5)-(10,4)-(11,6)- ... by the cells of the multiplication table generates the beginning of this sequence, therefore: a(0) = 1*1 = 1, a(1) = 2*3 = 6, a(2) = 4*2 = 8, a(3) = 5*4 = 20. CROSSREFS Cf. A001651 (route abscissas), A052938 (route ordinates). Cf. A000567, A003991 (multiplication table) Sequence in context: A199884 A028331 A279729 * A309653 A113806 A105775 Adjacent sequences: A357943 A357944 A357945 * A357947 A357948 A357949 KEYWORD nonn,easy AUTHOR Nicolay Avilov, Oct 21 2022 STATUS approved

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Last modified May 27 02:37 EDT 2024. Contains 372847 sequences. (Running on oeis4.)