A038765 Next-to-last diagonal of A024462.

1, 2, 7, 24, 81, 270, 891, 2916, 9477, 30618, 98415, 314928, 1003833, 3188646, 10097379, 31886460, 100442349, 315675954, 990074583, 3099363912, 9685512225, 30218798142, 94143178827, 292889889684, 910050728661, 2824295364810

Offset

0,2

Comments

If w is a binary string of length 2n-1 and v(w) is a vector of the Hamming weights of each substring of length n, then a(n) is the number of distinct v(w) for all possible w. - Orson R. L. Peters, Jun 01 2017

References

S. J. Cyvin et al., Unbranched catacondensed polygonal systems containing hexagons and tetragons, Croatica Chem. Acta, 69 (1996), 757-774.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Maths.SE, Number of different counts of 1s in sliding windows.

Index entries for linear recurrences with constant coefficients, signature (6,-9).

Formula

G.f.: (1-2*x)^2/(1-3*x)^2. [Detlef Pauly (dettodet(AT)yahoo.de), Mar 03 2003]

a(n) = 6*a(n-1)-9*a(n-2) for n>2. a(n) = 3^(n-2)*(n+5) for n>0. [Colin Barker, Jun 25 2012]

Maple

seq(ceil(1/9*3^n*(5+n)), n=0..50);

Mathematica

CoefficientList[Series[(1 - 2 x)^2/(1 - 3 x)^2, {x, 0, 30}], x] (* Vincenzo Librandi, Oct 22 2013 *)
LinearRecurrence[{6, -9}, {1, 2, 7}, 30] (* Harvey P. Dale, Jul 04 2018 *)

Prog

(Magma) [1] cat [3^(n-2)*(n+5): n in [1..30]]; // Vincenzo Librandi, Oct 22 2013

Crossrefs

Cf. A024462.

Sequence in context: A109682 A215694 A027124 * A027126 A027128 A099463

Adjacent sequences: A038762 A038763 A038764 * A038766 A038767 A038768

Keyword

nonn,easy

Author

N. J. A. Sloane, May 03 2000

Extensions

More terms from James A. Sellers, May 03 2000

Status

approved