OFFSET
3,2
COMMENTS
LINKS
Heinrich Ludwig, Table of n, a(n) for n = 3..100
Heinrich Ludwig, Illustration of tiling a 4X4X4 area
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = (n^4 - 6*n^3 + 5*n^2 + 30*n - 54)/2, n>=3.
From Colin Barker, May 12 2017: (Start)
G.f.: 3*x^4*(3 + x + x^2 - x^3) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>7.
(End)
EXAMPLE
There are 9 ways of tiling a triangular area of side 4 with two tiles of side 2 and an appropriate number (= 8) of tiles of side 1. See example in links section.
PROG
(PARI) concat(0, Vec(3*x^4*(3 + x + x^2 - x^3) / (1 - x)^5 + O(x^60))) \\ Colin Barker, May 12 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Heinrich Ludwig, May 10 2017
STATUS
approved