A210460 Expansion of x*(1+x)/(1-x-2*x^2-2*x^3-x^4).

1, 2, 4, 10, 23, 53, 123, 285, 660, 1529, 3542, 8205, 19007, 44030, 101996, 236275, 547334, 1267906, 2937120, 6803875, 15761261, 36511157, 84578549, 195927260, 453867933, 1051390708, 2435559643, 5642004185, 13069772820, 30276291184

Offset: 1

Author

Perminova Maria, Jan 22 2013

Keywords

• nonn
• easy

Comments

Transform of Fibonacci numbers based on the triangle A030528.

Links

• Index entries for linear recurrences with constant coefficients, signature (1,2,2,1).

Crossrefs

Cf. A000045, A030528, A123392.

Programs

Magma

[&+[Fibonacci(k)*Binomial(k,n-k): k in [Floor((n-1)/2)+1..n]]: n in [1..30]]; // Bruno Berselli, Jan 23 2013

Mathematica

CoefficientList[Series[(1 + x)/(1 - x - 2 x^2 - 2 x^3 - x^4), {x, 0, 30}], x] (* Bruno Berselli, Jan 23 2013 *)
LinearRecurrence[{1,2,2,1},{1,2,4,10},30] (* Harvey P. Dale, Mar 28 2015 *)

Formula

a(n) = sum(Fibonacci(k)*binomial(k,n-k), k=floor((n-1)/2)+1..n).

G.f.: x*(1+x)/(1-x-2*x^2-2*x^3-x^4).

a(n) = A123392(n-1)+A123392(n-2). [Bruno Berselli, Jan 23 2013]