OFFSET
1,3
COMMENTS
Consider the partitions of n into two distinct parts (p,q) where p < q. Then a(n) is the total area of the family of rectangles (and the areas of the squares on their sides) with dimensions p and |q - p|.
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).
FORMULA
a(n) = Sum_{i=1..floor((n-1)/2)} i*(n-2*i) + 2*i^2 + 2*(n-2*i)^2.
From Colin Barker, Apr 23 2019: (Start)
G.f.: x^3*(5 + 7*x + 8*x^2 + 2*x^3) / ((1 - x)^4*(1 + x)^3).
a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 3*a(n-4) + 3*a(n-5) + a(n-6) - a(n-7) for n>7.
(End)
MATHEMATICA
Table[(2 n - 3 - (-1)^n) (22 n^2 - 21 n + 5 n (-1)^n)/96, {n, 50}]
PROG
(PARI) concat([0, 0], Vec(x^3*(5 + 7*x + 8*x^2 + 2*x^3) / ((1 - x)^4*(1 + x)^3) + O(x^40))) \\ Colin Barker, Apr 23 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Apr 16 2018
STATUS
approved