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A085570
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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).
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0
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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
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