A027950 a(n) = T(2n,n+2), T given by A027948.

1, 6, 63, 344, 1383, 4685, 14323, 41119, 113590, 306605, 816410, 2157046, 5674578, 14893364, 39040633, 102273950, 267839033, 701315739, 1836198205, 4807389285, 12586103720, 32951083211, 86267338468, 225851160284, 591286410708, 1548008385490

Offset: 2

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 2..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-26,45,-45,26,-8,1).

Crossrefs

Bisection of A053739.

Cf. A000045, A027948.

Programs

GAP

Concatenation([1], List([3..40], n-> Fibonacci(2*n+6) -(48 +47*n +23*n^2 +4*n^3 +4*n^4)/6) ); # G. C. Greubel, Sep 29 2019

Magma

[1] cat [Fibonacci(2*n+6) -(48 +47*n +23*n^2 +4*n^3 +4*n^4)/6: n in [3..40]]; // G. C. Greubel, Sep 29 2019

Maple

with(combinat); seq(`if`(n=2,1, fibonacci(2*n+6) -(48 +47*n +23*n^2 +4*n^3 +4*n^4)/6), n=2..40); # G. C. Greubel, Sep 29 2019

Mathematica

Table[If[n==2, 1, Fibonacci[2*n+6] -(48 +47*n +23*n^2 +4*n^3 +4*n^4)/6], {n,2,40}] (* G. C. Greubel, Sep 29 2019 *)
CoefficientList[Series[x^2(1-2x+41x^2-49x^3+44x^4-26x^5+8x^6-x^7)/ ((1-3x+x^2)(1-x)^5),{x,0,30}],x] (* or *) LinearRecurrence[{8,-26,45,-45,26,-8,1},{1,6,63,344,1383,4685,14323,41119},30] (* Harvey P. Dale, Aug 15 2021 *)

PARI

Vec(x^2*(x^7-8*x^6+26*x^5-44*x^4+49*x^3-41*x^2+2*x-1)/((x-1)^5* (x^2-3*x+1)) + O(x^40)) \\ Colin Barker, Nov 19 2014

PARI

vector(40, n, my(m=n+1); if(m==2, 1, fibonacci(2*m+6) -(48 +47*m +23*m^2 +4*m^3 +4*m^4)/6) ) \\ G. C. Greubel, Sep 29 2019

Sage

[1]+[fibonacci(2*n+6) -(48 +47*n +23*n^2 +4*n^3 +4*n^4)/6 for n in (3..40)] # G. C. Greubel, Sep 29 2019

Formula

G.f.: x^2*(1-2*x+41*x^2-49*x^3+44*x^4-26*x^5+8*x^6-x^7)/((1-3*x+x^2)*(1-x)^5). - Ralf Stephan, Apr 24 2004

From G. C. Greubel, Sep 29 2019: (Start)

a(n) = Sum_{j=0..n-2} binomial(2*n-j, j+5), with a(2) = 1 for n >= 2.

a(n) = Fibonacci(2*n+6) - (48 + 47*n + 23*n^2 + 4*n^3 + 4*n^4)/6 for n >= 3. (End)

Extensions

More terms from Colin Barker, Nov 19 2014