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A123908 Number of sequences with terms 1, 2 or 3 summing to n with no three consecutive 1's. 1
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

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,1,2,2,1).

FORMULA

a(n) = a(n-2) + 2*a(n-3) + 2*a(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]:=1; a[1]:=1; a[2]:=2; a[3]:=3; a[4]:=6; for n from 5 to 45 do a[n] := a[n-2] +2*a[n-3] +2*a[n-4] +a[n-5] end do; seq(a[n], n = 0 .. 40); # modified by G. C. Greubel, Aug 06 2019

seq(coeff(series((1+x+x^2)/(1-x^2-2*x^3-2*x^4-x^5), x, n+1), x, n), n = 0 .. 40); # G. C. Greubel, Aug 06 2019

MATHEMATICA

LinearRecurrence[{0, 1, 2, 2, 1}, {1, 1, 2, 3, 6}, 40] (* G. C. Greubel, Aug 06 2019 *)

PROG

(PARI) my(x='x+O('x^40)); Vec((1+x+x^2)/(1-x^2-2*x^3-2*x^4-x^5)) \\ G. C. Greubel, Aug 06 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x+x^2)/(1-x^2-2*x^3-2*x^4-x^5) )); // G. C. Greubel, Aug 06 2019

(Sage) ((1+x+x^2)/(1-x^2-2*x^3-2*x^4-x^5)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Aug 06 2019

(GAP) a:=[1, 1, 2, 3, 6];; for n in [6..40] do a[n]:=a[n-2]+2*a[n-3]+ 2*a[n-4]+a[n-5]; od; a; # G. C. Greubel, Aug 06 2019

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 September 19 02:37 EDT 2019. Contains 327186 sequences. (Running on oeis4.)