A244521 -id:A244521 - cp's OEIS frontend

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

N. J. A. Sloane, Jul 20 2014

			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;
  ...

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.

Row sums are A244521(n+1).

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)<Andrew Howroyd, Mar 01 2020

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

A245437 Expansion of x^5/(x^6-x^4-x^2-x+1).

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 1, 2, 3, 6, 10, 17, 29, 50, 86, 147, 252, 432, 741, 1270, 2177, 3732, 6398, 10968, 18802, 32232, 55255, 94723, 162382, 278369, 477204, 818064, 1402395, 2404105, 4121322, 7065122, 12111635, 20762798, 35593360, 61017175, 104600848, 179315699

Offset: 0

Vincenzo Librandi, Jul 22 2014

G.f. taken from p. 12 of the Brlek et al. reference.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
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).
Index entries for linear recurrences with constant coefficients, signature (1,1,0,1,0,-1).

Cf. A079500, A175331, A244521, A245185.

[n le 6 select Floor(n/6) else Self(n-1)+Self(n-2)+Self(n-4)-Self(n-6): n in [1..50]];

CoefficientList[Series[x^5/(x^6 - x^4 - x^2 - x + 1), {x, 0, 50}], x]
LinearRecurrence[{1, 1, 0, 1, 0, -1}, {0, 0, 0, 0, 0, 1}, 50] (* Bruno Berselli, Jul 22 2014 *)

G.f.: x^5/(x^6 - x^4 - x^2 - x + 1).

a(n) = a(n-1) + a(n-2) + a(n-4) - a(n-6) for n>5.

cp's OEIS Frontend

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

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Extensions

A245437 Expansion of x^5/(x^6-x^4-x^2-x+1).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

Formula