OFFSET
1,2
LINKS
Delbert L. Johnson, Table of n, a(n) for n = 1..20000
Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).
FORMULA
a(n) = a(n-2) + n*(n-1) for n > 2, a(1)=1, a(2)=2.
G.f.: x*(1 - x^3 + 3*x^2 - x)/((x + 1)*(x - 1)^4). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009
a(n) + a(n+1) = A064999(n). - R. J. Mathar, Feb 27 2016
a(n) = n*(n + 2)*(2*n - 1)/12 + 3*(1 - (-1)^n)/8. - Bruno Berselli, Mar 12 2018
EXAMPLE
From Bruno Berselli, Mar 12 2018: (Start)
n=1: 1;
n=2: 1*2;
n=3: 1 + 0*1 + 2*3 = 7;
n=4: 1*2 + 3*4 = 14;
n=5: 1 + 0*1 + 2*3 + 4*5 = 27;
n=6: 1*2 + 3*4 + 5*6 = 44;
n=7: 1 + 0*1 + 2*3 + 4*5 + 6*7 = 69, etc.
(End)
MATHEMATICA
LinearRecurrence[{3, -2, -2, 3, -1}, {1, 2, 7, 14, 27}, 50] (* Vincenzo Librandi, Feb 28 2016 *)
PROG
(Magma) [n le 2 select n else Self(n-2)+n*(n-1):n in [1..50]]; // Vincenzo Librandi, Feb 28 2016
(C#) public BigInteger a(BigInteger n) => (n * (n + 2) * (2 * n - 1) + 9) / 12; // Delbert L. Johnson, Mar 19 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jon Wild, Jul 14 1997
EXTENSIONS
More terms from Erich Friedman
STATUS
approved