OFFSET
0,4
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-1,-3,2).
FORMULA
a(n) = (2^(n+3) - 5*(-1)^n - 3*(2*n+1))/12.
a(n+2) = a(n+1) + 2*a(n) + n, a(0)=0, a(1)=1.
G.f.: x*(1 - 2*x + 2*x^2)/(1 - 3*x + x^2 + 3*x^3 - 2*x^4). - Colin Barker, Jan 16 2012
MATHEMATICA
LinearRecurrence[{3, -1, -3, 2}, {0, 1, 1, 4}, 40] (* G. C. Greubel, May 25 2019 *)
PROG
(PARI) concat(0, Vec(x*(1-2*x+2*x^2)/(1-3*x+x^2+3*x^3-2*x^4) + O(x^40))) \\ G. C. Greubel, May 25 2019
(Magma) I:=[0, 1, 1, 4]; [n le 4 select I[n] else 3*Self(n-1)-Self(n-2) - 3*Self(n-3)+2*Self(n-4): n in [1..40]]; // G. C. Greubel, May 25 2019
(Sage) (x*(1-2*x+2*x^2)/(1-3*x+x^2+3*x^3-2*x^4)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, May 24 2019
(GAP) a:=[0, 1, 1, 4];; for n in [5..40] do a[n]:=3*a[n-1]-a[n-2]-3*a[n-3] +2*a[n-4]; od; a; # G. C. Greubel, May 24 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, May 01 2003
STATUS
approved