A083693 Sum of absolute values of list generated by n replacements of k by {-1-|k|, .., 1+|k|} with increment 2, starting with {1}.

1, 4, 18, 72, 324, 1360, 6280, 27296, 128784, 573760, 2752032, 12485248, 60652608, 278988032, 1368979584, 6365514240, 31488733440, 147697177600, 735486927360, 3474529986560, 17398140748800, 82683153633280, 415966710171648

Offset

0,2

Comments

Sum of absolute values of list elements starting from 0, (A083691), gives twice A083693, but with an initial zero.

Links

Table of n, a(n) for n=0..22.

Formula

A083691(n+2)/2-A083691(n+1)

Example

0, 1 and 2 substitutions produce lengths 1, 3 and 10:
{1}; {-2,0,2}; {-3,-1,1,3, -1,1, -3,-1,1,3} with sums of absolute values 1,4,18.

Mathematica

Table[Plus@@Abs@Flatten[Nest[ #/.k_Integer:>Table[i, {i, -1-Abs[k], Abs[k]+1, 2}]&, {1}, w]], {w, 0, 10}]

Crossrefs

Cf. A083691, A083692.

Sequence in context: A117615 A267450 A199524 * A123476 A343580 A027905

Adjacent sequences: A083690 A083691 A083692 * A083694 A083695 A083696

Keyword

nonn

Author

Wouter Meeussen, May 03 2003

Status

approved