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A120741 a(n) = (7^n - 1)/2. 2
0, 3, 24, 171, 1200, 8403, 58824, 411771, 2882400, 20176803, 141237624, 988663371, 6920643600, 48444505203, 339111536424, 2373780754971, 16616465284800, 116315256993603, 814206798955224, 5699447592686571, 39896133148806000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Number of compositions of odd natural numbers into n parts < 7. - Adi Dani, Jun 11 2011

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Adi Dani, Restricted compositions of natural numbers

Index entries for linear recurrences with constant coefficients, signature (8,-7).

FORMULA

a(n) = A034494(n) - 1.

a(n) = 8*a(n-1) - 7*a(n-2), n >= 2.

a(n) = right term in M^n * [1,0], where M is the 2 X 2 matrix [4,3; 3,4].

EXAMPLE

From Adi Dani, Jun 11 2011: (Start)

a(2)=24: there are 24 compositions of odd numbers into 2 parts < 7:

1: (0,1), (1,0);

3: (0,3), (3,0), (1,2), (2,1);

5: (0,5), (5,0), (1,4), (4,1), (2,3), (3,2);

7: (1,6), (6,1), (2,5), (5,2), (3,4), (4,3);

9: (3,6), (6,3), (4,5), (5,4);

11: (5,6),(6,5).  (End)

a(4) = 1200 = A034494(4) - 1, where A034494(4) = 1201.

a(4) = 1200 = 8*a(3) - 7*a(2) = 8*171 - 7*24.

a(4) = 1200 = right term in M^n * [1,0] = [A034494(4), a(4)] = [1201, 1200].

MATHEMATICA

Table[1/2*(7^n - 1), {n, 0, 25}]

PROG

(MAGMA) [(7^n-1)/2: n in [0..25]]; // Vincenzo Librandi, Jun 11 2011

(PARI) a(n)=7^n\2 \\ Charles R Greathouse IV, Jun 11 2011

CROSSREFS

Cf. A034494.

Sequence in context: A104527 A058038 A089697 * A292293 A073985 A197209

Adjacent sequences:  A120738 A120739 A120740 * A120742 A120743 A120744

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Jun 30 2006

EXTENSIONS

Complete edit by Joerg Arndt, Jun 11 2011

STATUS

approved

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Last modified November 28 07:52 EST 2021. Contains 349401 sequences. (Running on oeis4.)