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A001507 a(n) is the number of c-nets with n+1 vertices and 2n+1 edges, n >= 1.
(Formerly M3132 N1270)
3
0, 0, 0, 3, 33, 338, 3580, 39525, 452865, 5354832, 65022840, 807560625, 10224817515, 131631305718, 1719292293940, 22743461653913, 304256251541865, 4111134671255120, 56049154766899216, 770325744569310630, 10664613057653024586, 148625522045319923940 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
R. C. Mullin and P. J. Schellenberg, The enumeration of c-nets via triangulations, J. Combin. Theory, 4 (1968), 259-276.
FORMULA
a(n) = A290326(n+1,n). - Sean A. Irvine, Sep 29 2015
PROG
(PARI)
A290326(n, k) = {
if (n < 3 || k < 3, return(0));
sum(i=0, k-1, sum(j=0, n-1,
(-1)^((i+j+1)%2) * binomial(i+j, i)*(i+j+1)*(i+j+2)/2*
(binomial(2*n, k-i-1) * binomial(2*k, n-j-1) -
4 * binomial(2*n-1, k-i-2) * binomial(2*k-1, n-j-2))));
};
vector(22, n, A290326(n+1, n)) \\ Gheorghe Coserea, Jul 28 2017
CROSSREFS
Cf. A290326.
Sequence in context: A221883 A002277 A332087 * A221162 A231594 A075835
KEYWORD
nonn
AUTHOR
EXTENSIONS
Corrected and extended by Sean A. Irvine, Sep 29 2015
Name changed by Gheorghe Coserea, Jul 23 2017
STATUS
approved

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)