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Search: id:A100191
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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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1
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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; listen)
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OFFSET
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1,2
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COMMENT
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Sequence generated from level 2 of the Pascal tetrahedron.
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REFERENCES
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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
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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
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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
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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
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Cf. A100190.
Sequence in context: A137195 A055916 A060579 this_sequence A123950 A026545 A041937
Adjacent sequences: A100188 A100189 A100190 this_sequence A100192 A100193 A100194
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 07 2004
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EXTENSIONS
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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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