A027953 a(0)=1, a(n) = Fibonacci(2n+4) - (2n+3).

1, 3, 14, 46, 133, 364, 972, 2567, 6746, 17690, 46345, 121368, 317784, 832011, 2178278, 5702854, 14930317, 39088132, 102334116, 267914255, 701408690, 1836311858, 4807526929, 12586268976, 32951280048, 86267571219, 225851433662

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-8,5,-1).

Crossrefs

Cf. A000045, A027948.

Programs

GAP

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

Magma

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

Maple

with(combinat); seq(`if`(n=0,1, fibonacci(2*n+4) -(3 +2*n)), n=0..40); # G. C. Greubel, Sep 29 2019

Mathematica

Join[{1},Table[Fibonacci[2n+4]-(2n+3),{n,30}]] (* or *) LinearRecurrence[ {5,-8,5,-1},{1,3,14,46,133},30] (* Harvey P. Dale, Oct 04 2017 *)

PARI

vector(40, n, my(m=n-1); if(m==0, 1, fibonacci(2*m+4) -(3 +2*m)) ) \\ G. C. Greubel, Sep 29 2019

Sage

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

Formula

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

G.f.: (1-2*x+7*x^2-5*x^3+x^4)/((1-3*x+x^2)*(1-x)^2). - Vladeta Jovovic, Mar 27 2003

a(n) = Sum_{j=0..n} binomial(2*n-j+1, j+2), with a(0)=1. - G. C. Greubel, Sep 29 2019

Extensions

More terms from Vladeta Jovovic, Mar 27 2003