OFFSET
4,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 4..1000
Index entries for linear recurrences with constant coefficients, signature (12,-64,201,-414,588,-588,414,-201,64,-12,1).
FORMULA
From G. C. Greubel, Sep 29 2019: (Start)
a(n) = Sum_{j=0..n-3} binomial(2*n-j, j+9), with a(4) = 1.
a(n) = Fibonacci(2*n+10) - (138600 +133530*n +63999*n^2 + 20286*n^3 + 5929*n^4 + 616*n^6 - 96*n^7 + 16*n^8)/2520.
G.f.: x^4*(1 - 2*x + 175*x^2 - 33*x^3 + 408*x^4 - 614*x^5 + 587*x^6 - 414*x^7 + 201*x^8 - 64*x^9 + 12*x^10 - x^11)/((1-x)^9*(1-3*x+x^2)). (End)
MAPLE
with(combinat); seq(`if`(n=4, 1, fibonacci(2*n+10) -(138600 +133530*n +63999*n^2 + 20286*n^3 +5929*n^4 +616*n^6 -96*n^7 +16*n^8)/2520), n=4..40); # G. C. Greubel, Sep 29 2019
MATHEMATICA
Table[If[n==4, 1, Fibonacci[2*n+10] - (138600 +133530*n +63999*n^2 + 20286*n^3 +5929*n^4 +616*n^6 -96*n^7 +16*n^8)/2520], {n, 4, 40}] (* G. C. Greubel, Sep 29 2019 *)
PROG
(PARI) vector(40, n, my(m=n+3); if(m==4, 1, fibonacci(2*m+10) -(138600 +133530*m +63999*m^2 + 20286*m^3 +5929*m^4 +616*m^6 -96*m^7 +16*m^8)/2520) ) \\ G. C. Greubel, Sep 29 2019
(Magma) [1] cat [Fibonacci(2*n+10) -(138600 +133530*n +63999*n^2 + 20286*n^3 +5929*n^4 +616*n^6 -96*n^7 +16*n^8)/2520: n in [5..40]]; // G. C. Greubel, Sep 29 2019
(Sage) [1]+[fibonacci(2*n+10) -(138600 +133530*n +63999*n^2 + 20286*n^3 +5929*n^4 +616*n^6 -96*n^7 +16*n^8)/2520 for n in (5..40)] # G. C. Greubel, Sep 29 2019
(GAP) Concatenation([1], List([5..40], n-> Fibonacci(2*n+10) -(138600 +133530*n +63999*n^2 + 20286*n^3 +5929*n^4 +616*n^6 -96*n^7 +16*n^8)/2520) ); # G. C. Greubel, Sep 29 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Terms a(23) onward added by G. C. Greubel, Sep 29 2019
STATUS
approved