OFFSET
2,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 2..1000
Index entries for linear recurrences with constant coefficients, signature (9,-34,71,-90,71,-34,9,-1).
FORMULA
G.f.: x^2*(1 -2*x +63*x^2 -70*x^3 +85*x^4 -71*x^5 +34*x^6 -9*x^7 +x^8)/( (1-x)^6*(1-3*x+x^2)). - Colin Barker, Nov 25 2014
From G. C. Greubel, Sep 30 2019: (Start)
a(n) = Sum_{j=0..n-2} binomial(2*n-j+1, j+6) for n >= 3.
a(n) = Fibonacci(2*n+8) - (630 +607*n +295*n^2 +90*n^3 +20*n^4 +8*n^5)/30 for n >= 3. (End)
MAPLE
with(combinat); seq(`if`(n=2, 1, fibonacci(2*n+8) -(630 +607*n +295*n^2 +90*n^3 +20*n^4 +8*n^5)/30), n=2..40); # G. C. Greubel, Sep 30 2019
MATHEMATICA
Table[If[n==2, 1, Fibonacci[2*n+8] - (630 +607*n +295*n^2 +90*n^3 +20*n^4 +8*n^5)/30], {n, 2, 40}] (* G. C. Greubel, Sep 30 2019 *)
PROG
(PARI) vector(40, n, my(m=n+1); if(m==2, 1, fibonacci(2*m+8) -(630 +607*m +295*m^2 +90*m^3 +20*m^4 +8*m^5)/30) ) \\ G. C. Greubel, Sep 30 2019
(Magma) [1] cat [Fibonacci(2*n+8) -(630 +607*n +295*n^2 +90*n^3 +20*n^4 +8*n^5)/30: n in [3..40]]; // G. C. Greubel, Sep 30 2019
(Sage) [1]+[fibonacci(2*n+8) -(630 +607*n +295*n^2 +90*n^3 +20*n^4 +8*n^5)/30 for n in (3..40)] # G. C. Greubel, Sep 30 2019
(GAP) Concatenation([1], List([3..40], n-> Fibonacci(2*n+8) -(630 +607*n +295*n^2 +90*n^3 +20*n^4 +8*n^5)/30) ); # G. C. Greubel, Sep 30 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Name corrected and terms a(22) onward by G. C. Greubel, Sep 30 2019
STATUS
approved