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A000987 Number of stochastic matrices of integers.
(Formerly M1793 N0707)
0
0, 1, 1, 2, 7, 32, 184, 1268, 10186, 93356, 960646, 10959452, 137221954, 1870087808, 27548231008, 436081302248, 7380628161076, 132975267434552, 2540593483517404, 51299775805464824, 1091447620966600804, 24401984084483685248, 571907754141520643296 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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

Table of n, a(n) for n=0..22.

H. Gupta, Enumeration of symmetric matrices, Duke Math. J., 35 (1968), vol 3, 653-659.

H. Gupta, Enumeration of symmetric matrices (annotated scanned copy).

FORMULA

a(0) = 0, a(1) = 1, a(n) = (n-2) * a(n-1) + A000985(n - 2), n >= 2. - Sean A. Irvine, Sep 24 2015

MATHEMATICA

(* b = A000985 *) Clear[a, b]; b[0] = 1; b[1] = 1; b[2] = 3; b[3] = 11; b[4] = 56; b[n_] := b[n] = (2*n-1)*b[n-1] - (n-2)*(n-1)*b[n-2] - (n-2)*(n - 1)*b[n-3] + (n-3)*(n-2)*(n-1)*b[(n-4)]/2; a[0] = 0; a[1] = 1; a[n_] := a[n] = (n-2)*a[n-1] + b[n-2]; Array[a, 22, 0] (* Jean-Fran├žois Alcover, Feb 15 2016, after Sean A. Irvine *)

CROSSREFS

Sequence in context: A198891 A000153 A006154 * A006957 A189780 A195983

Adjacent sequences:  A000984 A000985 A000986 * A000988 A000989 A000990

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Sean A. Irvine, Sep 24 2015

STATUS

approved

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Last modified August 30 06:47 EDT 2016. Contains 275967 sequences.