OFFSET
3,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 3..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,1,-3,3,-1).
FORMULA
a(n) = (n + 3)*(2*n^2 + 9*n + 22)/30 - 1/5 - (-1/25*((5 - 5^(1/2))^(1/2) - (5 + 5^(1/2))^(1/2))*2^(1/2))*sin(2*n*Pi/5) - (1/25*((5 - 5^(1/2))^(1/2) + (5 + 5^(1/2))^(1/2))*2^(1/2))*sin(4*n*Pi/5). - Richard Choulet, Dec 14 2008
a(n) = round((2*n-1)*(n^2-n+6)/30) = floor((2*n^3-3*n^2+13*n)/30) = ceiling((n-1)*(2*n^2-n+12)/30) = round((n-1)*(2*n^2-n+12)/30). - Mircea Merca, Dec 03 2010
From R. J. Mathar, May 24 2010: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-5) - 3*a(n-6) + 3*a(n-7) - a(n-8).
G.f.: -x^3*(-2+2*x-2*x^2+x^3-2*x^4+3*x^5-3*x^6+x^7) / ( (x^4+x^3+x^2+x+1)*(x-1)^4 ). (End)
a(n) = a(n-5) + n^2 - 6*n + 13, n > 5, a(1)=0, a(2)=1. - Mircea Merca, Dec 03 2010
MATHEMATICA
f[n_] := Round[(2 n - 1)*(n^2 - n + 6)/30]; Array[f, 57, 3]
LinearRecurrence[{3, -3, 1, 0, 1, -3, 3, -1}, {2, 4, 8, 13, 21, 31, 44, 61}, 60] (* Harvey P. Dale, Sep 05 2023 *)
PROG
(Magma) [Round((2*n-1)*(n^2-n+6)/30): n in [3..60]]; // Vincenzo Librandi, Jun 25 2011
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved