A245185 Triangle read by rows: T(n,k) = number of pseudo-square parallelogram (psp) polyominoes with semiperimeter n+1 and k columns.

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 5, 2, 1, 1, 3, 7, 7, 3, 1, 1, 3, 11, 15, 11, 3, 1, 1, 4, 15, 25, 25, 15, 4, 1, 1, 4, 20, 41, 52, 41, 20, 4, 1, 1, 5, 25, 62, 92, 92, 62, 25, 5, 1, 1, 5, 32, 89, 159, 179, 159, 89, 32, 5, 1, 1, 6, 38, 122, 249, 342, 342, 249, 122, 38, 6, 1

Offset

1,8

Links

Andrew Howroyd, Table of n, a(n) for n = 1..300

Srecko Brlek, Andrea Frosini, Simone Rinaldi, Laurent Vuillon, Tilings by translation: enumeration by a rational language approach, The Electronic Journal of Combinatorics, vol. 13, (2006). See Table 2.

Example

Triangle begins:
  1;
  1, 1;
  1, 1,  1;
  1, 2,  2,  1;
  1, 2,  5,  2,  1;
  1, 3,  7,  7,  3,  1;
  1, 3, 11, 15, 11,  3,  1;
  1, 4, 15, 25, 25, 15,  4, 1;
  1, 4, 20, 41, 52, 41, 20, 4, 1;
  ...

Prog

(PARI)
IsPos(v)={for(i=1, #v, if(v[i]<=0, return(0))); 1}
E(b)={my(v=vector(hammingweight(b)-1), h=0, k=0); if(bittest(b, 0), b>>=1); while(k<#v, if(bittest(b, 0), k++; v[k]=h, h++); b>>=1); v}
Row(n)={my(v=vector(n)); forstep(b=2^n, 2*2^n, 2, my(r=E(b), d=b); for(k=1, n, d=bitor(d>>1, bitand(d, 1)<<n); if(bittest(d, 0) && !bittest(d, n), v[1+#r]+=IsPos(r-E(d))))); v}
{ for(n=1, 10, print(Row(n))) } \\ Andrew Howroyd, Mar 01 2020

Crossrefs

Row sums are A244521(n+1).

Sequence in context: A104156 A070166 A131373 * A034853 A242093 A350910

Adjacent sequences: A245182 A245183 A245184 * A245186 A245187 A245188

Keyword

nonn,tabl

Author

N. J. A. Sloane, Jul 20 2014

Extensions

Name clarified and terms a(46) and beyond from Andrew Howroyd, Mar 01 2020

Status

approved