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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
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
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.)