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A048460
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Total of odd numbers in the generations from 2 onwards.
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3
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2, 3, 3, 3, 4, 6, 5, 3, 4, 6, 6, 6, 8, 12, 9, 3, 4, 6, 6, 6, 8, 12, 10, 6, 8, 12, 12, 12, 16, 24, 17, 3, 4, 6, 6, 6, 8, 12, 10, 6, 8, 12, 12, 12, 16, 24, 18, 6, 8, 12, 12, 12, 16, 24, 20, 12, 16, 24, 24, 24, 32, 48, 33, 3, 4, 6, 6, 6, 8, 12, 10, 6, 8, 12, 12, 12, 16, 24, 18, 6, 8, 12, 12, 12, 16
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OFFSET
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2,1
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LINKS
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FORMULA
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It appears that a(n) = A105321(n)/2. - Omar E. Pol, May 29 2010. Proof from Nathaniel Johnston, Nov 07 2010: If you remove every 2nd row from Pascal's triangle then the rule for constructing the parity of the next row from the current row is the same as the rule for constructing generation n+1 of the primes from generation n: add up the previous and next term in the current row.
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EXAMPLE
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a(7)=6 because in generation 7 there are six odd numbers: 127,237,403,729,879,1109.
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MAPLE
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A048460 := proc(nmax) local par, c, r, prevc, prevl, cpar; par := [[], [1, 1]] ; for c from 3 to nmax do prevc := op(-1, par) ; prevl := nops(prevc) ; if nops(prevc) < 2 then cpar := [0] ; else cpar := [op(2, prevc)] ; end if; for r from 2 to prevl-1 do cpar := [op(cpar), ( op(r-1, prevc) + op(r+1, prevc)) mod 2] ; end do: cpar := [op(cpar), op(prevl-1, prevc), 1] ; par := [op(par), cpar] ; end do: cpar := [] ; for c from 2 to nops(par) do add(r, r=op(c, par)) ; cpar := [op(cpar), %] ; end do: cpar ; end proc: A048460(120) ; # R. J. Mathar, Aug 07 2010
nmax := 86: A001316 := n -> if n <=- 1 then 0 else 2^add(i, i=convert(n, base, 2)) fi: for p from 0 to ceil(simplify(log[2](nmax))) do for n from 2 to nmax/(p+2) do a((2*n-3)*2^p) := (2^(p-1)+1)*A001316(n-2) od: od: seq(a(n), n=2..nmax); # Johannes W. Meijer, Jan 22 2013
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MATHEMATICA
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A105321[n_] := Sum[Binomial[1, n-k] Mod[Binomial[k, j], 2], {k, 0, n}, {j, 0, k}];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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