OFFSET
3,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 3..1000
Index entries for linear recurrences with constant coefficients, signature (10,-43,105,-161,161,-105,43,-10,1).
FORMULA
From G. C. Greubel, Sep 28 2019: (Start)
a(n) = Sum_{j=0..n-3} binomial(2*n-j+1, 2*(n-j-3)).
a(n) = Fibonacci(2*n+9) - (8*n^6 + 12*n^5 + 110*n^4 + 465*n^3 + 1412*n^2 + 2943*n + 3060)/90.
G.f.: x^3*(1 + 27*x + 49*x^2 - 7*x^3 - 6*x^4)/((1-x)^7*(1-3*x+x^2)). (End)
MAPLE
with(combinat); seq(fibonacci(2*n+9) -(8*n^6 +12*n^5 +110*n^4 +465*n^3 +1412*n^2 + 2943*n +3060)/90, n=3..30); # G. C. Greubel, Sep 28 2019
MATHEMATICA
Table[Fibonacci[2*n+5] -(8*n^6 +12*n^5 +110*n^4 +465*n^3 +1412*n^2 + 2943*n +3060)/90, {n, 3, 30}] (* G. C. Greubel, Sep 28 2019 *)
PROG
(PARI) vector(30, n, my(m=n+2); fibonacci(2*m+9) - (8*m^6 +12*m^5 +110*m^4 +465*m^3 +1412*m^2 + 2943*m +3060)/90) \\ G. C. Greubel, Sep 28 2019
(Magma) [Fibonacci(2*n+9) - (8*n^6 +12*n^5 +110*n^4 +465*n^3 +1412*n^2 + 2943*n +3060)/90: n in [3..30]]; // G. C. Greubel, Sep 28 2019
(Sage) [fibonacci(2*n+9) - (8*n^6 +12*n^5 +110*n^4 +465*n^3 +1412*n^2 + 2943*n +3060)/90 for n in (3..30)] # G. C. Greubel, Sep 28 2019
(GAP) List([3..30], n-> Fibonacci(2*n+9) - (8*n^6 +12*n^5 +110*n^4 +465*n^3 +1412*n^2 + 2943*n +3060)/90 ); # G. C. Greubel, Sep 28 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Terms a(22) onward added by G. C. Greubel, Sep 28 2019
STATUS
approved