A137787 a(n) = 5^n - 4^n - 3^n - 2^n.

-2, -4, -4, 26, 272, 1826, 10736, 59426, 318272, 1670786, 8656976, 44454626, 226827872, 1151991746, 5830280816, 29429454626, 148249811072, 745630312706, 3745590106256, 18797445635426, 94264432179872, 472428649241666, 2366562219717296, 11850466059333026, 59322887352366272

Offset

0,1

Links

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (14,-71,154,-120).

Formula

G.f.: 2*(53*x^3-45*x^2+12*x-1)/((2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)). - Colin Barker, Oct 27 2014

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

E.g.f.: exp(2*x)*(exp(3*x) - exp(2*x) - exp(x) - 1).

a(n) = 14*a(n-1) - 71*a(n-2) + 154*a(n-3) - 120*a(n-4) for n > 3. (End)

Mathematica

Array[5^#-4^#-3^#-2^#&, 30, 0]
LinearRecurrence[{14, -71, 154, -120}, {-2, -4, -4, 26}, 30] (* Harvey P. Dale, Mar 25 2024 *)

Prog

(PARI) Vec(2*(53*x^3-45*x^2+12*x-1)/((2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)) + O(x^100)) \\ Colin Barker, Oct 27 2014

Crossrefs

Sequence in context: A068554 A371373 A092524 * A225171 A320600 A360685

Adjacent sequences: A137784 A137785 A137786 * A137788 A137789 A137790

Keyword

sign,easy,changed

Author

Vladimir Joseph Stephan Orlovsky, Apr 28 2008

Extensions

More terms, corrected offset and Mathematica program, Harvey P. Dale, Apr 27 2013

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

Status

approved