A052207 Number of sequences {s(i): i=0..n} such that |s(i)-s(i-1)|=1, i=1..n and s(i)=0 at four values of i, one of which is i=0.

0, 0, 0, 0, 0, 8, 16, 40, 80, 168, 336, 672, 1344, 2640, 5280, 10296, 20592, 40040, 80080, 155584, 311168, 604656, 1209312, 2351440, 4702880, 9152528, 18305056, 35659200, 71318400, 139070880, 278141760, 542911320, 1085822640, 2121460200, 4242920400, 8297266560

Offset

1,6

Comments

Calculation suggests that {a(2n)/8} is A002054 (shifted).

Links

Table of n, a(n) for n=1..36.

Sean A. Irvine, Java program (github)

Example

a(6) = 8: [0,-1,0,-1,0,-1,0], [0,-1,0,-1,0,1,0], [0,-1,0,1,0,-1,0], [0,-1,0,1,0,1,0], [0,1,0,-1,0,-1,0], [0,1,0,-1,0,1,0], [0,1,0,1,0,-1,0], [0,1,0,1,0,1,0].

Maple

a:= n-> max(0, (m-> 8*(d+1)*binomial(2*m+1, m-1))(iquo(n-4, 2, 'd'))):
seq(a(n), n=1..36);  # Alois P. Heinz, Oct 30 2021

Crossrefs

Cf. A002054.

Sequence in context: A269513 A024700 A108576 * A038578 A348925 A155110

Adjacent sequences: A052204 A052205 A052206 * A052208 A052209 A052210

Keyword

nonn

Author

John W. Layman, Jan 26 2000

Extensions

More terms from Sean A. Irvine, Oct 29 2021

Status

approved