A027951 a(n) = T(2n,n+3), T given by A027948.

1, 8, 129, 967, 4950, 20175, 70954, 226007, 672959, 1914166, 5280288, 14275838, 38102976, 100888126, 265838881, 698489013, 1832277574, 4802042229, 12578921258, 32941567397, 86254888591, 225835057708, 591265802288, 1547982265500, 4052706300752

Offset: 3

Author

Clark Kimberling

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A000045, A027948.

Programs

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

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

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 *)

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

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

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)

Extensions

More terms from Colin Barker, Nov 19 2014