OFFSET
0,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..2500
Richard Choulet, Curtz-like transformation.
Index entries for linear recurrences with constant coefficients, signature (3,-3,4,-2,1).
FORMULA
O.g.f.: ((1-z)^2/(1-3*z+2*z^2-z^3))*(1/(1+z^2))+((1-z+z^2)/(1-3*z+2*z^2-z^3)).
a(n) = 3*a(n-1) - 3*a(n-2) + 4*a(n-3) - 2*a(n-4) + a(n-5) for n>=5, with a(0)=2, a(1)=3, a(2)=6, a(3)=16, a(4)=39.
MAPLE
a(0):=2: a(1):=3:a(2):=6: a(3):=16:a(4):=39:for n from 0 to 31 do a(n+5):=3*a(n+4)-3*a(n+3)+4*a(n+2)-2*a(n+1)+a(n):od:seq(a(i), i=0..31);
MATHEMATICA
LinearRecurrence[{3, -3, 4, -2, 1}, {2, 3, 6, 16, 39}, 50] (* G. C. Greubel, Jun 17 2018 *)
PROG
(PARI) m=32; v=concat([2, 3, 6, 16, 39], vector(m-5)); for(n=6, m, v[n] = 3*v[n-1] -3*v[n-2] +4*v[n-3] -2*v[n-4] +v[n-5]); v \\ G. C. Greubel, Jun 17 2018
(Magma) I:=[2, 3, 6, 16, 39]; [n le 5 select I[n] else 3*Self(n-1) -3*Self(n-2) +4*Self(n-3) -2*Self(n-4) +Self(n-5): n in [1..50]]; // G. C. Greubel, Jun 17 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Richard Choulet, Apr 11 2009
STATUS
approved