A027954 a(n) = T(2n+1, n+2), T given by A027948.

1, 5, 41, 189, 674, 2098, 6050, 16703, 44995, 119575, 315460, 829060, 2174596, 5698329, 14924829, 39081553, 102326310, 267905078, 701397990, 1836299475, 4807512695, 12586252715, 32951261576, 86267550344, 225851410184, 591286703533, 1548008726545, 4052739505253, 10610209821610

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (7,-19,26,-19,7,-1).

Formula

G.f.: x*(1 -2*x +25*x^2 -29*x^3 +19*x^4 -7*x^5 +x^6)/((1-x)^4*(1 -3*x +x^2)). - Colin Barker, Nov 25 2014

From G. C. Greubel, Sep 30 2019: (Start)

a(n) = Sum_{j=0..n-1} binomial(2*n-j+1, j+4) for n >= 2.

a(n) = Fibonacci(2*n+6) - (24 + 23*n + 12*n^2 + 4*n^3)/3 for n >= 2. (End)

Maple

with(combinat); seq(`if`(n=1, 1, fibonacci(2*n+6) -(24 +23*n +12*n^2 +4*n^3)/3), n=1..40); # G. C. Greubel, Sep 30 2019

Mathematica

Table[If[n==1, 1, Fibonacci[2*n+6] - (24 +23*n +12*n^2 +4*n^3)/3], {n, 1, 40}] (* G. C. Greubel, Sep 30 2019 *)

Prog

(PARI) vector(40, n, if(n==1, 1, fibonacci(2*n+6) -(24 +23*n +12*n^2 + 4*n^3)/3 )) \\ G. C. Greubel, Sep 30 2019
(Magma) [1] cat [Fibonacci(2*n+6) -(24 + 23*n + 12*n^2 + 4*n^3)/3: n in [2..40]]; // G. C. Greubel, Sep 30 2019
(Sage) [1]+[fibonacci(2*n+6) -(24 + 23*n + 12*n^2 + 4*n^3)/3 for n in (2..40)] # G. C. Greubel, Sep 30 2019
(GAP) Concatenation([1], List([2..40], n-> Fibonacci(2*n+6) -(24 + 23*n + 12*n^2 + 4*n^3)/3 )); # G. C. Greubel, Sep 30 2019

Crossrefs

Cf. A000045, A027948.

Sequence in context: A271001 A258229 A096946 * A270623 A322420 A270165

Adjacent sequences: A027951 A027952 A027953 * A027955 A027956 A027957

Keyword

nonn

Author

Clark Kimberling

Extensions

Name corrected and terms a(22) onward by G. C. Greubel, Sep 30 2019

Status

approved