login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 9 09:37 EST 2021. Contains 349627 sequences. (Running on oeis4.)