A081684 a(n) = 5^n - 4^n - 3^n - 2^n + 3.

1, -1, -1, 29, 275, 1829, 10739, 59429, 318275, 1670789, 8656979, 44454629, 226827875, 1151991749, 5830280819, 29429454629, 148249811075, 745630312709, 3745590106259, 18797445635429, 94264432179875, 472428649241669, 2366562219717299, 11850466059333029, 59322887352366275, 296896476647946629

Offset: 0

Author

Paul Barry, Mar 30 2003

Keywords

• easy
• sign

Comments

Inverse binomial transform of A081685.

Links

• Index entries for linear recurrences with constant coefficients, signature (15,-85,225,-274,120).

Crossrefs

Cf. A081685.

Programs

Mathematica

Table[5^n-4^n-3^n-2^n+3,{n,0,40}]  (* Harvey P. Dale, Apr 01 2011 *)

Formula

G.f.: (-1-254*x^4+266*x^3-99*x^2+16*x)/((x-1)*(4*x-1)*(3*x-1)*(2*x-1)*(5*x-1)) [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009]

From Elmo R. Oliveira, Sep 12 2024: (Start)

E.g.f.: exp(x)*(exp(4*x) - exp(3*x) - exp(2*x) - exp(x) + 3).

a(n) = 15*a(n-1) - 85*a(n-2) + 225*a(n-3) - 274*a(n-4) + 120*a(n-5) for n > 4. (End)

Extensions

a(24)-a(25) from Elmo R. Oliveira, Sep 12 2024