A194773 Number of lower triangles of an (n+4) X (n+4) 0..3 array with new values introduced in row major order 0..3 and no element unequal to more than one horizontal or vertical neighbor.
43, 105, 265, 655, 1641, 4069, 10121, 25025, 61809, 152019, 372979, 912017, 2224175, 5408825, 13120905, 31752431, 76673045, 184762437, 444388957, 1066954113, 2557518625, 6121119363, 14629468735, 34918297649, 83242029523, 198212839881
Offset: 1
Keywords
Examples
All solutions for 5 X 5 including a 3: 0 0 1 1 1 1 1 1 2 1 1 1 1 1 2 2 2 2 2 2 1 1 2 2 3 2 2 2 2 3
Links
- R. H. Hardin, Table of n, a(n) for n = 1..27
Crossrefs
Cf. A194778.
Formula
Empirical: a(n) = 5*a(n-1) -2*a(n-2) -22*a(n-3) +21*a(n-4) +35*a(n-5) -34*a(n-6) -26*a(n-7) +15*a(n-8) +9*a(n-9).
Empirical g.f.: x*(43 - 110*x - 174*x^2 + 486*x^3 + 303*x^4 - 706*x^5 - 310*x^6 + 318*x^7 + 153*x^8) / ((1 - x)*(1 - x - x^2)^2*(1 - x - 3*x^2)^2). - Colin Barker, May 05 2018
Comments