A140498 a(n) = 3*a(n-1)-3*a(n-2)+3*a(n-3) with a(0)=1, a(1)=3, a(2)=7.

1, 3, 7, 15, 33, 75, 171, 387, 873, 1971, 4455, 10071, 22761, 51435, 116235, 262683, 593649, 1341603, 3031911, 6851871, 15484689, 34994187, 79084107, 178723827, 403901721, 912786003, 2062824327, 4661820135, 10535345433, 23809048875, 53806570731, 121598601867

Offset: 0

Author

Paul Curtz, Jun 29 2008

Keywords

• nonn
• easy

Comments

Second differences of A137256.

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-3,3).

Crossrefs

Cf. A137256.

Programs

Magma

m:=32; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+x^2)/(1-3*x+3*x^2-3*x^3))); // Bruno Berselli, Mar 28 2012

Mathematica

LinearRecurrence[{3,-3,3},{1,3,7},32] (* or *) CoefficientList[Series[(1+x^2)/(1-3*x+3*x^2-3*x^3),{x,0,31}],x] (* James C. McMahon, Jul 11 2025 *)

Formula

G.f.: (1+x^2)/(1-3*x+3*x^2-3*x^3). - Colin Barker, Mar 28 2012

Extensions

More terms from Colin Barker, Mar 28 2012