A134396 A007318 * A000125.

1, 3, 9, 27, 80, 232, 656, 1808, 4864, 12800, 33024, 83712, 208896, 514048, 1249280, 3002368, 7143424, 16842752, 39387136, 91422720, 210763776, 482869248, 1099956224, 2492465152, 5620367360, 12616466432, 28202500096, 62797119488, 139318001664, 308029685760

Offset: 0

Author

Gary W. Adamson, Oct 23 2007

Keywords

• nonn
• easy

Comments

a(n) is the number of ternary strings of length n that contain at most three 0's.- Enrique Navarrete, Mar 13 2024

Examples

			a(3) = 27 = (1, 3, 3, 1) dot (1, 2, 4, 8) = (1 + 6 + 12 + 8), where A000125 = (1, 2, 4, 8, 15, 26, 42, ...).
a(3) = 27 = sum of row 3 terms of triangle A134395: (8 + 12 + 6 + 1).
		

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-24,32,-16).

Crossrefs

Cf. A134395, A000125.

Programs

Mathematica

CoefficientList[Series[(1-x)(1-4x+5x^2)/(1-2x)^4,{x,0,30}],x] (* or *) LinearRecurrence[ {8,-24,32,-16},{1,3,9,27},30] (* Harvey P. Dale, Mar 09 2023 *)

PARI

Vec((1-x)*(1-4*x+5*x^2) / (1-2*x)^4 + O(x^30)) \\ Colin Barker, Feb 13 2017

Formula

Binomial transform of A000125. Row sums of triangle A134395.

O.g.f.: (1-x)*(1-4*x+5*x^2) / (1-2*x)^4. - R. J. Mathar, Jun 08 2008

From Colin Barker, Feb 13 2017: (Start)

a(n) = 8*a(n-1) - 24*a(n-2) + 32*a(n-3) - 16*a(n-4) for n>3.

a(n) = (2^(n-4)*(48 + 20*n + 3*n^2 + n^3)) / 3. (End)

E.g.f.: e^(2*x)*(1+x+x^2/2+x^3/6). - Enrique Navarrete, Mar 13 2024

Extensions

More terms from R. J. Mathar, Jun 08 2008