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A100191
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The (1,1)-entry in the 3 X 3 matrix M^n, where M=[1,2,1/2,2,0/1,0,0] (n>=1).
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0
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1, 6, 19, 73, 264, 973, 3565, 13086, 48007, 176149, 646296, 2371321, 8700553, 31923030, 117128107, 429752305, 1576795176, 5785386229, 21227039605, 77883687150, 285761407807, 1048481205661, 3846960466104, 14114802199681
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Sequence generated from level 2 of the Pascal tetrahedron.
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REFERENCES
| Peter Hilton, Derek Holton and Jean Pederson, "Mathematical Vistas, From a Room With Many Windows"; Springer, 2000, p. 178, Fig. 14, "The Pascal Tetrahedron".
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FORMULA
| a(n)=3a(n-1)+3a(n-2)-2a(n-3) (derived from the minimal polynomial of the matrix M).
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EXAMPLE
| a(4)=73 because M^4 = [73,86,19 / 86,104,24 / 19,24,6]. Alternatively, a(4)=3a(3)+3a(2)-2a(1)=57+18-2=73.
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MAPLE
| with(linalg): M[1]:=matrix(3, 3, [1, 2, 1, 2, 2, 0, 1, 0, 0]): for n from 2 to 27 do M[n]:=multiply(M[1], M[n-1]) od: seq(M[n][1, 1], n=1..27);
a[1]:=1: a[2]:=6: a[3]:=19: for n from 4 to 27 do a[n]:=3*a[n-1]+3*a[n-2]-2*a[n-3] od: seq(a[n], n=1..27);
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CROSSREFS
| Cf. A100190.
Sequence in context: A060579 A183326 * A123950 A191585 A026545 A041937
Adjacent sequences: A100188 A100189 A100190 * A100192 A100193 A100194
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 07 2004
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EXTENSIONS
| Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 07 2006
Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 04 2006
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