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 A048460 Total of odd numbers in the generations from 2 onwards. 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 LINKS FORMULA 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. a((2*n-3)*2^p) = (2^(p-1)+1)*A001316(n-2), p >= 0 and n >= 2. - Johannes W. Meijer, Jan 22 2013 EXAMPLE a(7)=6 because in generation 7 there are six odd numbers: 127,237,403,729,879,1109. MAPLE 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 :=  ; 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(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 CROSSREFS For "Generations" see A048448-A048455. See also A047844. Cf. A220466. Sequence in context: A029068 A108932 A029067 * A351058 A036017 A029066 Adjacent sequences: A048457 A048458 A048459 * A048461 A048462 A048463 KEYWORD nonn AUTHOR Patrick De Geest, May 15 1999 EXTENSIONS More terms from R. J. Mathar, Aug 07 2010 STATUS approved

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Last modified March 31 14:53 EDT 2023. Contains 361665 sequences. (Running on oeis4.)