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A137402 a(n) = Sum_{k=0..n} binomial(floor(n-2k/3), k). 2
1, 1, 2, 3, 5, 9, 16, 28, 48, 81, 136, 229, 388, 661, 1129, 1928, 3287, 5594, 9510, 16164, 27484, 46757, 79577, 135454, 230552, 392355, 667620, 1135924, 1932721, 3288563, 5595805, 9522067, 16203273, 27572144, 46917243, 79834375, 135845607, 231154212 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A_n + B_{n-1} + C_{n-2} in the notation of A137356.

REFERENCES

D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.4.

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,1).

FORMULA

a(0)=1, a(1)=1, a(2)=2, a(3)=3, a(4)=5, a(n) = 3*a(n-1)-3*a(n-2)+a(n-3)+ a(n-5). - Harvey P. Dale, Aug 22 2011

G.f.: (1-2*x+2*x^2-x^3+x^4) / (1-3*x+3*x^2-x^3-x^5). - Colin Barker, Dec 14 2015

MAPLE

f:=n->add( binomial( floor(n-2*k/3), k), k=0..n);

MATHEMATICA

Table[Sum[Binomial[Floor[n-(2k)/3], k], {k, 0, n}], {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1, 0, 1}, {1, 1, 2, 3, 5}, 40] (* Harvey P. Dale, Aug 22 2011 *)

PROG

(PARI) Vec((1-2*x+2*x^2-x^3+x^4)/(1-3*x+3*x^2-x^3-x^5) + O(x^50)) \\ Colin Barker, Dec 14 2015

(PARI) a(n) = sum(k=0, n, binomial(floor(n-2*k/3), k)); \\ Altug Alkan, Dec 14 2015

CROSSREFS

Sequence in context: A119968 A291311 A017914 * A134009 A018160 A079960

Adjacent sequences:  A137399 A137400 A137401 * A137403 A137404 A137405

KEYWORD

nonn,easy

AUTHOR

Don Knuth, Apr 11 2008

STATUS

approved

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Last modified October 22 02:46 EDT 2018. Contains 316431 sequences. (Running on oeis4.)