OFFSET
1,1
REFERENCES
See formula for enumeration of contacts in Fulton-Kleiman-MacPherson (pp. 156-196 of Lect. Notes Math. n.997).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
William Fulton, Steven Kleiman, Robert MacPherson, About the enumeration of contacts, Algebraic Geometry — Open Problems, Lecture Notes in Mathematics, 1983 vol. 997.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = n^3 + 3*n^2 + 3*n - 3.
G.f.: x*(4 + 7*x - 8*x^2 + 3*x^3)/(1-x)^4. - Colin Barker, Sep 03 2012
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Wesley Ivan Hurt, Oct 20 2022
MATHEMATICA
LinearRecurrence[{4, -6, 4, -1}, {4, 23, 60, 121}, 40] (* Harvey P. Dale, Nov 29 2014 *)
PROG
(Magma) [n^3+3*n^2+3*n-3: n in [1..45]]; // Vincenzo Librandi, Jun 30 2011
(PARI) a(n)=n^3 + 3*n^2 + 3*n - 3 \\ Charles R Greathouse IV, Feb 10 2017
CROSSREFS
KEYWORD
nonn,nice,easy
AUTHOR
Paolo Dominici (pl.dm(AT)libero.it)
STATUS
approved