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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
3,4
COMMENTS
Row indices n begin with 3, column indices k begin with 0.
LINKS
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
Sequence in context: A293520 A292602 A071444 * A328701 A085257 A352889
KEYWORD
nonn,tabl
AUTHOR
L. Edson Jeffery, Nov 23 2013
STATUS
approved

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Last modified March 28 07:33 EDT 2024. Contains 371235 sequences. (Running on oeis4.)