OFFSET
0,2
COMMENTS
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..10000 (corrected and extended original b-file from Colin Barker after data change).
John King, Star a=6, 84 matches, 118 triangles
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = n*(10*n^2+9*n+1) = 2*A045950(n).
From Colin Barker, Apr 04 2019: (Start)
G.f.: 2*x*(10 + 19*x + x^2) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3. (End)
E.g.f.: exp(x)*x*(20 + 39*x + 10*x^2). - Stefano Spezia, Sep 20 2024
EXAMPLE
For n=1, there are 12 (size=1) + 6 (size=4) + 2 (size=9) = 20 triangles.
MATHEMATICA
LinearRecurrence[{4, -6, 4, -1}, {0, 20, 118, 354}, 50] (* Paolo Xausa, Sep 18 2024 *)
PROG
(PARI) concat(0, Vec(2*x*(10 + 19*x + x^2) / (1 - x)^4 + O(x^40))) \\ Colin Barker, Apr 04 2019
CROSSREFS
KEYWORD
nonn,easy,less
AUTHOR
John King, Feb 22 2018
EXTENSIONS
STATUS
approved