OFFSET
0,3
COMMENTS
For n >=1, a(n) is the number of divisions of a 2 X n board into 3 pieces. See Jacob Brown article.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..10000
Jacob Brown, Counting Divisions of a 2 X n Rectangular Grid, arXiv:2106.14755 [math.CO], 2021.
Tomislav Došlić and Luka Podrug, Sweet division problems: from chocolate bars to honeycomb strips and back, arXiv:2304.12121 [math.CO], 2023.
Samuel Durham and Tom Richmond, Connected Subsets of an n X 2 Rectangle, The College Mathematics Journal, Volume 51, 2020 - Issue 1.
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
From Chai Wah Wu, Jun 29 2021: (Start)
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 4.
G.f.: (1 - 5*x + 14*x^2 - x^3 + 7*x^4)/(1-x)^5. (End)
MATHEMATICA
CoefficientList[Series[(1 - 5 x + 14 x^2 - x^3 + 7 x^4)/(1 - x)^5, {x, 0, 38}], x] (* Michael De Vlieger, Apr 28 2023 *)
PROG
(PARI) a(n) = 2*n^4/3 - 4*n^3/3 + 11*n^2/6 - 13*n/6 + 1;
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michel Marcus, Jun 29 2021
STATUS
approved