A085569
Denominator of 2*Sum(C(n,w)/(2*w+1),w=0..n/2-1)+C(n,n/2)/(n+1) if n is even, or of 2*Sum(C(n,w)/(2*w+1),w=0..(n-1)/2) if n is odd.
Original entry on oeis.org
1, 1, 3, 1, 15, 3, 7, 15, 45, 5, 231, 21, 455, 315, 45, 3, 1683, 3465, 7315, 5005, 3003, 143, 13455, 585, 6825, 13923, 3213, 6545, 515185, 17765, 110143, 31977, 2078505, 62985, 1789515, 51129, 210197, 426075, 246675, 6325, 1400355, 34155, 41612175, 84192075
Offset: 0
1, 2, 8/3, 4, 88/15, 28/3, 104/7, 376/15, 1904/45, 372/5, 30152/231, ...
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b := binomial; f1 := n->if n mod 2 = 0 then 2*add(b(n,w)/(2*w+1),w=0..n/2-1)+b(n,n/2)/(n+1); else 2*add(b(n,w)/(2*w+1),w=0..(n-1)/2); fi;
A085570
If n mod 2 = 0 then 2*Sum(floor(C(n,w)/(2*w+1)),w=0..n/2-1)+floor(C(n,n/2)/(n+1)) otherwise 2*Sum(floor(C(n,w)/(2*w+1)),w=0..(n-1)/2).
Original entry on oeis.org
1, 2, 2, 4, 5, 8, 14, 24, 39, 74, 128, 232, 423, 776, 1426, 2660, 4931, 9268, 17346, 32840, 61903, 117832, 223410, 427156, 813812, 1561830, 2987535, 5751742, 11039759, 21312036, 41025866, 79386066, 153208323, 297072312, 574604611, 1116186954, 2163216427
Offset: 0
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b := binomial; f2 := n->if n mod 2 = 0 then 2*add(floor(b(n,w)/(2*w+1)),w=0..n/2-1)+floor(b(n,n/2)/(n+1)); else 2*add(floor(b(n,w)/(2*w+1)),w=0..(n-1)/2); fi;
A085571
Numerator of 2*Sum(C(n,w)/w,w=1..n/2-1)+C(n,n/2)/(n/2) if n is even otherwise of 2*Sum(C(n,w)/w,w=1..(n-1)/2).
Original entry on oeis.org
2, 6, 11, 20, 101, 175, 593, 173, 1502, 2684, 28649, 52169, 662393, 1224077, 4506259, 4210067, 23506871, 44294491, 41572193, 78849257, 1639049932, 3125022742, 23750582143, 9095291663, 225666905951, 144544431373, 276913262539, 76244134117, 732674442397
Offset: 2
2, 6, 11, 20, 101/3, 175/3, 593/6, 173, 1502/5, 2684/5, 28649/30, ...
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b := binomial; f3 := n->if n mod 2 = 0 then 2*add(b(n,w)/w,w=1..n/2-1)+b(n,n/2)/(n/2); else 2*add(b(n,w)/w,w=1..(n-1)/2); fi;
A085572
Denominator of 2*Sum(C(n,w)/w,w=1..n/2-1)+C(n, n/2)/(n/2) if n is even otherwise of 2*Sum(C(n,w)/w,w=1..(n-1)/2).
Original entry on oeis.org
1, 1, 1, 1, 3, 3, 6, 1, 5, 5, 30, 30, 210, 210, 420, 210, 630, 630, 315, 315, 3465, 3465, 13860, 2772, 36036, 12012, 12012, 1716, 8580, 8580, 17160, 8580, 145860, 204204, 612612, 612612, 11639628, 11639628, 29099070, 29099070, 29099070, 29099070, 1322685, 14549535
Offset: 2
2, 6, 11, 20, 101/3, 175/3, 593/6, 173, 1502/5, 2684/5, 28649/30, ...
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b := binomial; f3 := n->if n mod 2 = 0 then 2*add(b(n,w)/w,w=1..n/2-1)+b(n, n/2)/(n/2); else 2*add(b(n,w)/w,w=1..(n-1)/2); fi;
A085573
2*Sum(floor(C(n,w)/w),w=1..n/2-1)+floor(C(n,n/2)/(n/2)) if n is even, otherwise 2*Sum(floor(C(n,w)/w),w=1..(n-1)/2).
Original entry on oeis.org
2, 6, 11, 20, 32, 56, 97, 172, 298, 534, 952, 1736, 3150, 5824, 10724, 20042, 37308, 70304, 131971, 250308, 473020, 901872, 1713596, 3281122, 6262254, 12033330, 23053047, 44431308, 85393280, 165008114, 318009610, 615878180, 1189803926, 2308781688
Offset: 2
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b := binomial; f3 := n->if n mod 2 = 0 then 2*add(floor(b(n,w)/w),w=1..n/2-1)+floor(b(n,n/2)/(n/2)); else 2*add(floor(b(n,w)/w),w=1..(n-1)/2); fi;
Showing 1-5 of 5 results.