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 (11,-53,148,-266,322,-266,148,-53,11,-1).
FORMULA
From G. C. Greubel, Sep 30 2019: (Start)
a(n) = Sum_{j=0..n-3} binomial(2*n-j+1, j+8) for n >= 4.
a(n) = Fibonacci(2*n+10) - (34650 +33360*n +16065*n^2 +5089*n^3 +1260*n^4 +280*n^5 +16*n^7)/630 for n >= 4.
G.f.: x^3*(1 -2*x +129*x^2 -78*x^3 +246*x^4 -329*x^5 +266*x^6 -148*x^7 +53*x^8 -11*x^9 +x^10)/((1-x)^8*(1-3*x+x^2)). (End)
MAPLE
with(combinat); seq(`if`(n=3, 1, fibonacci(2*n+10) -(34650 +33360*n +16065*n^2 +5089*n^3 +1260*n^4 +280*n^5 +16*n^7)/630), n=3..40); # G. C. Greubel, Sep 30 2019
MATHEMATICA
Table[If[n==3, 1, Fibonacci[2*n+10] -(34650 +33360*n +16065*n^2 +5089*n^3 +1260*n^4 +280*n^5 +16*n^7)/630], {n, 3, 40}] (* G. C. Greubel, Sep 30 2019 *)
LinearRecurrence[{11, -53, 148, -266, 322, -266, 148, -53, 11, -1}, {1, 9, 175, 1518, 8735, 39130, 148487, 502415, 1568062, 4622488, 13091798}, 40] (* Harvey P. Dale, Sep 12 2021 *)
PROG
(PARI) vector(40, n, my(m=n+2); if(m==3, 1, fibonacci(2*m+10) -(34650 +33360*m +16065*m^2 +5089*m^3 +1260*m^4 +280*m^5 +16*m^7)/630) ) \\ G. C. Greubel, Sep 30 2019
(Magma) [1] cat [Fibonacci(2*n+10) -(34650 +33360*n +16065*n^2 +5089*n^3 +1260*n^4 +280*n^5 +16*n^7)/630: n in [4..40]]; // G. C. Greubel, Sep 30 2019
(Sage) [1]+[fibonacci(2*n+10) -(34650 +33360*n +16065*n^2 +5089*n^3 +1260*n^4 +280*n^5 +16*n^7)/630 for n in (4..40)] # G. C. Greubel, Sep 30 2019
(GAP) Concatenation([1], List([4..40], n-> Fibonacci(2*n+10) -(34650 +33360*n +16065*n^2 +5089*n^3 +1260*n^4 +280*n^5 +16*n^7)/630) ); # 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