A075115 Binomial transform of A073145: a(n)=Sum(binomial(n,k)*A073145(k),(k=0,..,n)).

3, 2, 0, 2, 8, 12, 12, 16, 32, 56, 80, 112, 176, 288, 448, 672, 1024, 1600, 2496, 3840, 5888, 9088, 14080, 21760, 33536, 51712, 79872, 123392, 190464, 293888, 453632, 700416, 1081344, 1669120, 2576384, 3977216, 6139904, 9478144, 14630912

Offset: 0

Author

Mario Catalani (mario.catalani(AT)unito.it), Sep 02 2002

Keywords

• easy
• nonn

Comments

a(n) is nonnegative since the real root of x^3-2*x^2+2*x-2 is dominant. - Michael Somos, Feb 28 2007

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..5303
• Yassine Otmani, The 2-Pascal Triangle and a Related Riordan Array, J. Int. Seq. (2025) Vol. 28, Issue 3, Art. No. 25.3.5. See p. 21.
• N. J. A. Sloane, Transforms
• Index entries for linear recurrences with constant coefficients, signature (2,-2,2).

Crossrefs

Cf. A073145, A073498.

Programs

Mathematica

CoefficientList[Series[(3-4*x+2*x^2)/(1-2*x+2*x^2-2*x^3), {x, 0, 40}], x]
LinearRecurrence[{2,-2,2},{3,2,0},40] (* Harvey P. Dale, Jan 24 2019 *)

PARI

{a(n)= if(n<0, 0, polsym( x^3 -2*x^2 +2*x -2, n) [n+1])} /* Michael Somos, Feb 28 2007 */

Formula

a(n)=2a(n-1)-2a(n-2)+2a(n-3), a(0)=3, a(1)=2, a(2)=0.

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

a(n) = 3*A077943(n) -4*A077943(n-1) +2*A077943(n-2). - R. J. Mathar, Mar 13 2021