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A030236 Cycle-path coverings of a family of digraphs. 1
1, 2, 7, 18, 49, 136, 377, 1044, 2891, 8006, 22171, 61398, 170029, 470860, 1303949, 3611016, 9999959, 27692810, 76689487, 212375610, 588130153, 1628704336, 4510358465, 12490501212, 34589849507, 95789405774, 265268869027 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

O. M. D'Antona and E. Munarini, The Cycle-path Indicator Polynomial of a Digraph, Advances in Applied Mathematics 25 (2000), 41-56.

LINKS

Table of n, a(n) for n=0..26.

FORMULA

a(n+4) = 3 a(n+3) - a(n+2) + a(n+1), n >= 0.

a(n+3) = 2*a(n+2) + a(n+1) + 2*sum( a(i), i = 0..n ), n >= 0.

G.f.: (1-x+2*x^2-2*x^3)/(1-3*x+x^2-x^3).

a(n) = sum(binomial(n+k+1,3*k+1)*2^k,k=0..n)+2*sum(binomial(n+k-1,3*k+1)*2^k,k=0..n-1). [Emanuele Munarini, Dec 03 2012]

PROG

(Maxima) makelist(sum(binomial(n+k+1, 3*k+1)*2^k, k, 0, n)+2*sum(binomial(n+k-1, 3*k+1)*2^k, k, 0, n-1), n, 0, 60); [Emanuele Munarini, Dec 03 2012]

CROSSREFS

Cf. A030186.

Sequence in context: A022726 A192873 A017925 * A074141 A122931 A094976

Adjacent sequences:  A030233 A030234 A030235 * A030237 A030238 A030239

KEYWORD

nonn,easy

AUTHOR

Ottavio D'Antona (dantona(AT)dsi.unimi.it) and Emanuele Munarini.

STATUS

approved

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Last modified October 16 00:50 EDT 2018. Contains 316252 sequences. (Running on oeis4.)