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Search: id:A157904
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| 1, 2, 4, 8, 17, 36, 78, 170, 375, 833, 1870, 4229, 9654, 22223, 51622, 120961, 286029, 682398, 1642821, 3990231, 9777678, 24166327, 60233185, 151350709, 383287499, 977918150, 2512805727, 6500178867, 16921248231, 44310852884, 116678914575
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OFFSET
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0,2
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FORMULA
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INVERT transform of A000055: (1, 1, 1, 1, 2, 3, 6, 11, 23, 47, 106,...).
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EXAMPLE
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a(3) = 8 = (1, 1, 1) dot (1, 2, 4) + 1 = 7 + 1 = 8; where the operation uses ascending terms of A000055: (1, 1, 1, 1, 2, 3, 6, 11,...) and an equal number of ongoing descending terms of A157904. Take the dot product and add to the next term of A000055. a(4) = 17 = (1, 1, 1, 1) dot (1, 2, 4, 8) + 2 = 15 + 2.
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MAPLE
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with (numtheory): b:= proc(n) option remember; local d, j; if n<=1 then n else (add (add (d*b(d), d= divisors(j)) *b(n-j), j=1..n-1))/ (n-1) fi end: t:= proc(n) option remember; local k; `if` (n=0, 1, b(n)- (add (b(k) *b(n-k), k=1..n-1) -`if` (type (n, odd), 0, b(n/2)))/2) end: a:= proc(n) option remember; local i; if n<=0 then 1 else add (t(i)*a(n-i-1), i=0..n) fi end: seq (a(n), n=0..35); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Mar 31 2009]
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CROSSREFS
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Cf. A000055, A157905
Sequence in context: A008999 A052903 A063457 this_sequence A002845 A072925 A002955
Adjacent sequences: A157901 A157902 A157903 this_sequence A157905 A157906 A157907
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 08 2009
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EXTENSIONS
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More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Mar 31 2009
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