|
|
A071300
|
|
Numerator of b(n) where b(n+1) = Sum_{k=0..n} b'((n^2-k^2)/n), b(0) = b(1) = 1, and b'(x) = b(x) if x is an integer and is linearly interpolated otherwise.
|
|
2
|
|
|
1, 1, 2, 9, 65, 82, 1111, 12707, 44127, 270757, 3324143, 773311279, 583426241, 51327727127, 1207458414241, 251022006941731, 1784247347470303, 542442461832071, 59337844204584969481, 172785053530529793211
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
EXAMPLE
|
b(4) = b'(9/3) + b'(8/3) + b'(5/3) + b'(0/3) = b(3) + ((1/3)*b(2) + (2/3)*b(3)) + ((1/3)*b(1) + (2/3)*b(2)) + b(0) = 65/6.
|
|
MAPLE
|
bp:= proc(x) local t; option remember; if x::integer then b(x)
else t:= frac(x); t*b(ceil(x))+(1-t)*b(floor(x))
fi
end proc:
b:= proc(m) local k; option remember; add(bp(((m-1)^2-k^2)/(m-1)), k=0..m-1); end proc:
b(0):= 1: b(1):= 1:
|
|
MATHEMATICA
|
bp[x_] := bp[x] = Module[{t}, If[IntegerQ[x], b[x],
t = FractionalPart[x]; t*b[Ceiling[x]] + (1-t)*b[Floor[x]]]];
b[m_] := b[m] = Sum[bp[((m-1)^2 - k^2)/(m-1)], {k, 0, m-1}];
b[0] = 1; b[1] = 1;
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy,frac
|
|
AUTHOR
|
Michele Dondi (blazar(AT)lcm.mi.infn.it), Jun 10 2002
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|