A083691 -id:A083691 - cp's OEIS frontend

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

Wouter Meeussen, May 03 2003

nonn

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

			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.

Cf. A083691, A083692.

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

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

A083692 Length of list generated by n replacements of k by {-1-|k|, .., 1+|k|} with increment 2, starting with {1}.

Original entry on oeis.org

1, 3, 10, 38, 148, 620, 2600, 11480, 50256, 229296, 1032352, 4816736, 22118720, 104890048, 488768128, 2346515840, 11058545920, 53605825280, 254908828160, 1245304583680, 5965139153920, 29328419056640, 141339991746560

Offset: 0

Wouter Meeussen, May 03 2003

nonn

Same sequence starting with {0}: see A083691. Sum of absolute values of list elements gives A083693. Cross-references cite sequences with similar generation by integer-substitution and length of resulting lists.

			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}

Cf. A000108, A001003, A006319.

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

Drop first 2 terms from A083691 and divide by 2.

cp's OEIS Frontend

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

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