OFFSET
3,2
LINKS
Colin Barker, 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
G.f.: x^3*(1 -2*x +92*x^2 -84*x^3 +148*x^4 -162*x^5 +105*x^6 -43*x^7 +10*x^8 -x^9)/((1-x)^7*(1-3*x+x^2)). - Colin Barker, Nov 19 2014
From G. C. Greubel, Sep 29 2019: (Start)
a(n) = Sum_{j=0..n-3} binomial(2*n-j, j+7), with a(3) = 1 for n >= 3.
a(n) = Fibonacci(2*n+8) - (8*n^6 -12*n^5 +110*n^4 +255*n^3 +872*n^2 +1827*n +1890)/90 for n >= 4. (End)
MAPLE
with(combinat); seq(`if`(n=3, 1, fibonacci(2*n+8) -(8*n^6 -12*n^5 +110*n^4 +255*n^3 +872*n^2 +1827*n +1890)/90), n=3..40); # G. C. Greubel, Sep 29 2019
MATHEMATICA
CoefficientList[Series[(x^9 -10x^8 +43x^7 -105x^6 +162x^5 -148x^4 +84x^3 -92x^2 +2x -1)/((x-1)^7(x^2-3x+1)), {x, 0, 40}], x] (* Vincenzo Librandi, Nov 20 2014 *)
Table[If[n==3, 1, Fibonacci[2*n+8] -(8*n^6 -12*n^5 +110*n^4 +255*n^3 +872*n^2 +1827*n +1890)/90], {n, 3, 40}] (* G. C. Greubel, Sep 29 2019 *)
PROG
(PARI) Vec(x^3*(x^9-10*x^8+43*x^7-105*x^6+162*x^5-148*x^4+84*x^3-92*x^2 +2*x-1)/((x-1)^7*(x^2-3*x+1)) + O(x^40)) \\ Colin Barker, Nov 19 2014
(PARI) vector(40, n, my(m=n+2); if(m==3, 1, fibonacci(2*m+8) -(8*m^6 -12*m^5 +110*m^4 +255*m^3 +872*m^2 +1827*m +1890)/90) ) \\ G. C. Greubel, Sep 29 2019
(Magma) [1] cat [Fibonacci(2*n+8) -(8*n^6 -12*n^5 +110*n^4 +255*n^3 +872*n^2 +1827*n +1890)/90: n in [4..40]]; // G. C. Greubel, Sep 29 2019
(Sage) [1]+[fibonacci(2*n+8) -(8*n^6 -12*n^5 +110*n^4 +255*n^3 +872*n^2 +1827*n +1890)/90 for n in (4..40)] # G. C. Greubel, Sep 29 2019
(GAP) Concatenation([1], List([4..40], n-> Fibonacci(2*n+8) -(8*n^6 -12*n^5 +110*n^4 +255*n^3 +872*n^2 +1827*n +1890)/90) ); # G. C. Greubel, Sep 29 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 19 2014
STATUS
approved