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A038765 Next-to-last diagonal of A024462. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 28 21:37 EDT 2020. Contains 334690 sequences. (Running on oeis4.)