A072674 a(n) = 3^n+2*2^n-3.

0, 4, 14, 40, 110, 304, 854, 2440, 7070, 20704, 61094, 181240, 539630, 1610704, 4815734, 14414440, 43177790, 129402304, 387944774, 1163310040, 3488881550, 10464547504, 31389448214, 94159956040, 282463090910, 847355718304

Offset

0,2

References

G. S. Carr, Formulas and Theorems in Pure Mathematics, New York, Chelsea, 1970. see pp. 83-84.

Links

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (6,-11,6).

Formula

G.f.: x * (4 - 10*x) / ((1 - x) * (1 - 2*x) * (1 - 3*x)).

a(0)=0, a(1)=4, a(2)=14, a(n)=6*a(n-1)-11*a(n-2)+6*a(n-3). - Harvey P. Dale, Sep 06 2012

Example

4*x + 14*x^2 + 40*x^3 + 110*x^4 + 304*x^5 + 854*x^6 + 2440*x^7 + 7070*x^8 + ...

Mathematica

Table[3^n+2*2^n-3, {n, 0, 30}] (* or *) LinearRecurrence[{6, -11, 6}, {0, 4, 14}, 30] (* Harvey P. Dale, Sep 06 2012 *)

Prog

(PARI) {a(n) = 3^n + 2 * 2^n - 3}

Crossrefs

Sequence in context: A001872 A054443 A281766 * A202900 A238117 A032285

Adjacent sequences: A072671 A072672 A072673 * A072675 A072676 A072677

Keyword

nonn,easy

Author

Michael Somos, Jul 01 2002

Status

approved