A103470 Number of polyominoes consisting of 4 regular unit n-gons.
3, 5, 7, 7, 7, 11, 14, 19, 23, 23, 23, 29, 35, 42, 48, 47, 48, 57, 64, 74, 82, 81, 82, 93, 103, 115, 125, 123, 125, 139, 150, 165, 177, 175, 177, 193, 207, 224, 238, 235, 238, 257, 272, 292, 308, 305, 308, 329, 347, 369, 387, 383, 387, 411, 430, 455, 475, 471, 475
Offset: 3
Examples
a(3)=3 because there are 3 polyiamonds consisting of 4 triangles and a(4)=5 because there are 5 polyominoes consisting of 4 squares.
Links
- Colin Barker, Table of n, a(n) for n = 3..1000
- S. Kurz, k-polyominoes.
- Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-2,2,-1,0,0,0,0,0,1,-2,2,-2,2,-2,1).
Programs
-
Mathematica
LinearRecurrence[{2,-2,2,-2,2,-1,0,0,0,0,0,1,-2,2,-2,2,-2,1},{3,5,7,7,7,11,14,19,23,23,23,29,35,42,48,47,48,57},80] (* Harvey P. Dale, Feb 11 2020 *) -
PARI
Vec(-x^3*(x^17 -2*x^16 +3*x^15 -4*x^14 +4*x^13 -4*x^12 +4*x^11 -2*x^10 +2*x^9 -2*x^8 +4*x^7 -x^6 +x^5 +3*x^4 -3*x^3 +3*x^2 -x +3)/((x -1)^3*(x +1)*(x^2 -x +1)^2*(x^2 +1)*(x^2 +x +1)^2*(x^4 -x^2 +1)) + O(x^100)) \\ Colin Barker, Jan 19 2015
Formula
See the link for a formula.
G.f.: -x^3*(x^17 -2*x^16 +3*x^15 -4*x^14 +4*x^13 -4*x^12 +4*x^11 -2*x^10 +2*x^9 -2*x^8 +4*x^7 -x^6 +x^5 +3*x^4 -3*x^3 +3*x^2 -x +3) / ((x -1)^3*(x +1)*(x^2 -x +1)^2*(x^2 +1)*(x^2 +x +1)^2*(x^4 -x^2 +1)). - Colin Barker, Jan 19 2015