OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
From Harvey P. Dale, Nov 06 2011: (Start)
a(n) = (3 + 28*n - 24*n^2 + 32*n^3)/3.
G.f.: (1+3*x)^3/(1-x)^4.
a(0)=1, a(1)=13, a(2)=73, a(3)=245, a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)
E.g.f.: (1/3)*(3 + 36*x + 72*x^2 + 32*x^3)*exp(x). - G. C. Greubel, May 26 2021
MATHEMATICA
Table[(3+28n-24n^2+32n^3)/3, {n, 0, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 13, 73, 245}, 40] (* Harvey P. Dale, Nov 06 2011 *)
PROG
(Magma) [(3+28*n-24*n^2+32*n^3)/3: n in [0..40]]; // Vincenzo Librandi, Nov 16 2011
(Sage) [(3+28*n-24*n^2+32*n^3)/3 for n in (0..40)] # G. C. Greubel, May 26 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 23 2003
STATUS
approved