A000501
a(n) = floor(cosh(n)).
Original entry on oeis.org
1, 1, 3, 10, 27, 74, 201, 548, 1490, 4051, 11013, 29937, 81377, 221206, 601302, 1634508, 4443055, 12077476, 32829984, 89241150, 242582597, 659407867, 1792456423, 4872401723, 13244561064, 36002449668, 97864804714, 266024120300, 723128532145, 1965667148572
Offset: 0
-
f := n->floor(evalf(cosh(n)));
-
Table[Floor[Cosh[n]], {n, 0, 50}] (* T. D. Noe, Jun 20 2012 *)
A309104
a(n) = Sum_{k >= 0} floor(n^(2*k+1) / (2*k+1)!).
Original entry on oeis.org
0, 1, 3, 9, 25, 72, 199, 545, 1487, 4048, 11007, 29930, 81371, 221199, 601295, 1634499, 4443044, 12077466, 32829974, 89241138, 242582585, 659407853, 1792456409, 4872401708, 13244561050, 36002449653, 97864804699, 266024120286, 723128532126, 1965667148555
Offset: 0
For n = 5:
- we have:
k 5^(2*k+1)/(2*k+1)!
- ------------------
0 5
1 20
2 26
3 15
4 5
5 1
>=6 0
- hence a(5) = 5 + 20 + 26 + 15 + 5 + 1 = 72.
-
f:= proc(n) local t,k,v;
v:= n; t:= n;
for k from 1 do
v:= v*n^2/(2*k*(2*k+1));
if v < 1 then return t fi;
t:= t + floor(v);
od
end proc:
map(f, [$0..30]); # Robert Israel, Mar 18 2020
-
a(n) = { my (v=0, d=n); forstep (k=2, oo, 2, if (d<1, return (v), v += floor(d); d *= n^2/(k*(k+1)))) }
A361669
a(n) = floor of sinh(sinh(sinh(...(1)...))) with n iterations.
Original entry on oeis.org
1, 1, 1, 2, 3, 22, 3355531547
Offset: 0
a(0) = 1,
a(1) = floor(sinh(1)) = floor(1.175...) = 1,
a(2) = floor(sinh(sinh(1))) = floor(1.465...) = 1,
a(3) = floor(sinh(sinh(sinh(1)))) = floor(2.048...) = 2,
a(4) = floor(sinh(sinh(sinh(sinh(1))))) = floor(3.812...) = 3,
a(5) = floor(sinh(sinh(sinh(sinh(sinh(1)))))) = floor(22.627...) = 22,
a(6) = floor(sinh(sinh(sinh(sinh(sinh(sinh(1))))))) = 3355531547.
-
a:= n-> floor(evalf((sinh@@n)(1), 45)):
seq(a(n), n=0..6); # Alois P. Heinz, Mar 20 2023
-
Table[Floor[Nest[Sinh[n],1,n]],{n,0,7}]
Showing 1-3 of 3 results.
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