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A123908 Number of sequences with terms 1, 2 or 3 summing to n with no three consecutive 1's. 0
1, 1, 2, 3, 6, 10, 17, 30, 52, 90, 156, 271, 470, 815, 1414, 2453, 4255, 7381, 12804, 22211, 38529, 66836, 115940, 201120, 348881, 605201, 1049837, 1821143, 3159121, 5480100, 9506282, 16490465, 28605867, 49622350, 86079461, 149321296 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..35.

FORMULA

a(n) = a(n - 2) + 2a(n - 3) + 2a(n - 4) + a(n - 5)

G.f.: (1 + x + x^2)/(1 - x^2 - 2*x^3 - 2*x^4 - x^5). - Chai Wah Wu, May 28 2016

EXAMPLE

a(4) = 6 as 3 + 1, 1 + 3, 2 + 2, 1 + 1 + 2, 1 + 2 + 1 and 2 + 1 + 1 (but not 1 + 1 + 1 + 1).

MAPLE

a[0]=a[1]=1 a[2]=2 a[3]=3 a[4]=6 a[n_] := a[n - 2] + 2a[n - 3] + 2a[n - 4] + a[n - 5]

CROSSREFS

Sequence in context: A245437 A285665 A135431 * A233268 A026397 A193200

Adjacent sequences:  A123905 A123906 A123907 * A123909 A123910 A123911

KEYWORD

easy,nonn

AUTHOR

Joel B. Lewis, Oct 28 2006

STATUS

approved

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Last modified July 23 05:58 EDT 2017. Contains 289686 sequences.