OFFSET
0,1
COMMENTS
Coefficient of x in the polynomial 6*(C(n,0) + C(n+1,1)x + C(n+2,2)x(x-1)/2 + C(n+3,3)x(x-1)(x-2)/6).
LINKS
Danny Rorabaugh, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = 3!(C(n+1, 1)-C(n+2, 2)/2+C(n+3, 3)/3) = (2n^3 + 3n^2 + 31n + 30)/6.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4), n>3. - Vincenzo Librandi, Sep 07 2015
a(n+1) = a(n) + A117951(n+1), a(0) = 5. - Altug Alkan, Sep 28 2015
MATHEMATICA
CoefficientList[Series[(5 - 9 x + 6 x^2)/(1 - x)^4, {x, 0, 45}], x] (* Vincenzo Librandi Sep 07 2015 *)
LinearRecurrence[{4, -6, 4, -1}, {5, 11, 20, 34}, 50] (* Harvey P. Dale, Dec 23 2018 *)
PROG
(PARI) Vec((5-9*x+6*x^2)/(1-x)^4 + O(x^60)) \\ Michel Marcus, Sep 06 2015
(Magma) [(2*n^3+3*n^2+31*n+30)/6: n in [0..50]]; // Vincenzo Librandi, Sep 07 2015
(PARI) a(n)=(2*n^3 + 3*n^2 + 31*n + 30)/6;
vector(40, n, a(n-1)) \\ Altug Alkan, Sep 28 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 01 2003
STATUS
approved