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A232441
Sequence read from antidiagonals of rectangular array given by A(n,k) = 2^(2*k)*(Sum_{j=1..n-floor(n/2)-1} (cos(j*Pi/n))^(2*k)), rows n >= 3, columns k >= 0.
1
1, 1, 1, 2, 2, 1, 2, 3, 4, 1, 3, 4, 7, 8, 1, 3, 5, 10, 18, 16, 1, 4, 6, 13, 28, 47, 32, 1, 4, 7, 16, 38, 82, 123, 64, 1, 5, 8, 19, 48, 117, 244, 322, 128, 1, 5, 9, 22, 58, 152, 370, 730, 843, 256, 1, 6, 10, 25, 68
OFFSET
3,4
COMMENTS
Row indices n begin with 3, column indices k begin with 0.
FORMULA
A(2*m+1,k) = A186740(m,k), m = 1,2,....
Conjecture: A(n,k) = floor(A198632(n-1,k)/2), n >= 3, k >= 0.
EXAMPLE
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,...
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024,...
2, 3, 7, 18, 47, 123, 322, 843, 2207, 5778,15127,...
2, 4, 10, 28, 82, 244, 730, 2188, 6562,19684,59050,...
MATHEMATICA
Table[Function[m, FullSimplify[2^(2 k)*Sum[Cos[j*Pi/m]^(2 k), {j, m - Floor[m/2] - 1}]]][n - k + 1], {n, 3, 12}, {k, 0, n - 2}] // Flatten (* Michael De Vlieger, Mar 18 2017 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
L. Edson Jeffery, Nov 23 2013
STATUS
approved