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

2,2

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).

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)

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 *)

Prog

(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
(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
(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
(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

Crossrefs

Bisection of A053739.

Cf. A000045, A027948.

Sequence in context: A339239 A055005 A027811 * A184447 A053700 A296393

Adjacent sequences: A027947 A027948 A027949 * A027951 A027952 A027953

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

More terms from Colin Barker, Nov 19 2014

Status

approved