A240199 Area under the path specified by n-th composition.

0, 1, 4, 3, 9, 8, 5, 6, 16, 15, 12, 13, 7, 8, 11, 10, 25, 24, 21, 22, 16, 17, 20, 19, 9, 10, 13, 12, 18, 17, 14, 15, 36, 35, 32, 33, 27, 28, 31, 30, 20, 21, 24, 23, 29, 28, 25, 26, 11, 12, 15, 14, 20, 19, 16, 17, 27, 26, 23, 24, 18

Offset

0,3

Comments

Compositions are in the order specified in A066099.

Path has run lengths given by the specified composition followed by its reversal.

Can be considered a table with row lengths A011782 (2^(n-1)).

Maximum in row n is n^2, for [n]; minimum is 2*n-1 for [1,n-1].

Links

Table of n, a(n) for n=0..60.

Example

Row 5 of A066099 is [2,1]. The path generated by [2,1,1,2] is:
__
  |_
    |
____|
The area under the path is 8, so a(5) = 8.

Prog

(PARI) A066099row(n) = {local(v=vector(n), j=0, k=0);
   while(n>0, k++; if(n%2==1, v[j++]=k; k=0); n\=2);
   vector(j, i, v[j-i+1])} \\ row n of A066099.
patharea(v) = {local(m=#v, n=sum(k=1, m, v[k]), w, r=0);
   w=vector(2*m, k, if(k<=m, v[k], v[2*m+1-k]));
   forstep(k=1, 2*m, 2, r+=w[k]*n; n-=w[k+1]);
   r}
a(n) = patharea(A066099row(n)) \\ Franklin T. Adams-Watters, Apr 02 2014

Crossrefs

Cf. A066099, A011782.

Sequence in context: A365323 A263193 A094885 * A094728 A212001 A365904

Adjacent sequences: A240196 A240197 A240198 * A240200 A240201 A240202

Keyword

nonn,tabf

Author

Franklin T. Adams-Watters, Apr 02 2014

Status

approved