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

Author

N. J. A. Sloane, May 03 2000

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A024462.

Programs

Magma

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

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 *)

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]

Extensions

More terms from James Sellers, May 03 2000