OFFSET
1,2
COMMENTS
a(n) is the sum of the elements of the multiplication table, forming the maximum diamond in its center.
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..10000
Nicolay Avilov, Drawing for a(1)-a(5)
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = n^2*(2*n^2 - 2*n + 1).
From Stefano Spezia, Sep 19 2022: (Start)
G.f.: x*(1 + 15*x + 27*x^2 + 5*x^3)/(1 - x)^5.
EXAMPLE
In the multiplication table [1..3] X [1..3]: a(2) = 2+2+4+6+6 = 20;
In the multiplication table [1..5] X [1..5]: a(3) = 3+4+3+6+6+8+9+8+12+12+15+16+15 = 117.
For n=3, the multiplication table [1..5] X [1..5] and the terms summed are
* 1 2 3 4 5
-----------------
1| 3
2| 4 6 8
3| 3 6 9 12 15
4| 8 12 16
5| 15
MATHEMATICA
LinearRecurrence[{5, -10, 10, -5, 1}, {1, 20, 117, 400, 1025}, 50] (* Paolo Xausa, Oct 03 2024 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Nicolay Avilov, Sep 18 2022
STATUS
approved