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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

Table of n, a(n) for n=2..86.

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 := [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

CROSSREFS

For "Generations" see A048448-A048455. See also A047844.

Cf. A220466.

Sequence in context: A029068 A108932 A029067 * A036017 A029066 A174522

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 June 26 02:24 EDT 2017. Contains 288749 sequences.