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A126099 Number of 3-indecomposable (connected) graphs on n nodes. 4
1, 1, 1, 2, 6, 21, 7, 10, 10, 15, 15, 21, 21, 28, 28, 36, 36, 45, 45, 55, 55, 66, 66, 78, 78, 91, 91, 105, 105, 120, 120, 136, 136, 153, 153, 171, 171, 190, 190, 210, 210, 231, 231, 253, 253, 276, 276, 300, 300, 325, 325, 351, 351, 378, 378, 406, 406, 435, 435, 465, 465, 496 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

See A124593 for definition.

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

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

FORMULA

G.f.: x/((1-x)*(1-x^2)^2) + 1 - x^3 + 3*x^4 + 15*x^5 + x^6.

From Colin Barker, May 27 2016: (Start)

a(n) = (-1+(-1)^n+2*(1+(-1)^n)*n+2*n^2)/16 for n>7.

a(n) = (n^2+2*n)/8 for n>7 and even.

a(n) = (n^2-1)/8 for n>7 and odd.

a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>12.

G.f.: x*(1-2*x^2+x^3+5*x^4+13*x^5-22*x^6-26*x^7+32*x^8+14*x^9-14*x^10-x^11) / ((1-x)^3*(1+x)^2).

(End)

MATHEMATICA

LinearRecurrence[{1, 2, -2, -1, 1}, {1, 1, 1, 2, 6, 21, 7, 10, 10, 15, 15, 21, 21}, 70] (* Harvey P. Dale, Sep 18 2019 *)

PROG

(PARI) Vec(x*(1-2*x^2+x^3+5*x^4+13*x^5-22*x^6-26*x^7+32*x^8+14*x^9-14*x^10-x^11) / ((1-x)^3*(1+x)^2) + O(x^50)) \\ Colin Barker, May 27 2016

CROSSREFS

Cf. A128526, A128527, A128528.

Sequence in context: A162682 A103160 A242819 * A063753 A066893 A004192

Adjacent sequences:  A126096 A126097 A126098 * A126100 A126101 A126102

KEYWORD

nonn,easy

AUTHOR

David Applegate and N. J. A. Sloane, Mar 05 2007

STATUS

approved

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Last modified April 19 17:46 EDT 2021. Contains 343117 sequences. (Running on oeis4.)