A075194 Binomial transform of pentanacci numbers A074048: a(n)=Sum((-1)^k*Binomial(n,k)*A074048(k),(k=0,..,n)).

5, 4, 6, 4, 6, 4, 0, -24, -82, -212, -454, -876, -1548, -2544, -3858, -5276, -6050, -4348, 3744, 25768, 75206, 174444, 357858, 673076, 1175972, 1909904, 2851270, 3789508, 4089238, 2255044, -4809280, -22969880, -62544962, -140412180, -281990486, -521513324, -896946156, -1432099056

Offset: 0

Author

Mario Catalani (mario.catalani(AT)unito.it), Sep 08 2002

Keywords

• easy
• sign

Links

• N. J. A. Sloane, Transforms
• Index entries for linear recurrences with constant coefficients, signature (4, -5, 0, 5, -4).

Crossrefs

Cf. A074048.

Programs

Mathematica

CoefficientList[Series[(5-16x+15x^2-5x^4)/(1-4x+5x^2-5x^4+4x^5), {x, 0, 40}], x]

Formula

a(n)=4a(n-1)-5a(n-2)+5a(n-4)-4a(n-5), a(0)=5, a(1)=4, a(2)=6, a(3)=4, a(4)=6. G.f.: (5-16x+15x^2-5x^4)/(1-4x+5x^2-5x^4+4x^5).