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Search: id:A122174
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| A122174 |
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First row sum of the matrix M^n, where M is the 5 X 5 matrix {{0,-1,-1,-1,-1}, {-1,0,-1,-1,0}, {-1,-1,0,0,0}, {-1,-1,0,1,0}, {-1,0,0,0,1}}. |
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+0
1
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| 1, -4, 6, -24, 41, -145, 273, -886, 1789, -5457, 11605, -33807, 74761, -210366, 479256, -1313465, 3061242, -8222492, 19501429, -51579259, 123983182, -324067194, 787044384, -2038584810, 4990387355, -12836179872, 31614557443, -80883958143, 200146505560, -509959672813
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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P. Steinbach, Golden fields: a case for the heptagon, Math. Mag. 70 (1997), no. 1, 22-31.
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FORMULA
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a(n)=2a(n-1)+5a(n-2)-13a(n-3)+7a(n-4)-a(n-5); a(0)=1, a(1)=-4, a(2)=6, a(3)=-24, a(4)=41 (follows from the minimal polynomial x^5-2x^4-5x^3+13x^2-7x+1 of the matrix M).
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MAPLE
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with(linalg): M[1]:=matrix(5, 5, [0, -1, -1, -1, -1, -1, 0, -1, -1, 0, -1, -1, 0, 0, 0, -1, -1, 0, 1, 0, -1, 0, 0, 0, 1]): for n from 2 to 30 do M[n]:=multiply(M[n-1], M[1]) od: 1, seq(M[n][1, 1]+M[n][1, 2]+M[n][1, 3]+M[n][1, 4]+M[n][1, 5], n=1..30);
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MATHEMATICA
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M = {{0, -1, -1, -1, -1}, {-1, 0, -1, -1, 0}, {-1, -1, 0, 0, 0}, {-1, -1, 0, 1, 0}, {-1, 0, 0, 0, 1}}; v[1] = {1, 1, 1, 1, 1}; v[n_] := v[n] = M.v[n - 1]; a1 = Table[v[n][[1]], {n, 1, 25}]
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CROSSREFS
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Cf. A046854. Cf. A046854. Cf. A007700, A059455. Cf. A065941.
Adjacent sequences: A122171 A122172 A122173 this_sequence A122175 A122176 A122177
Sequence in context: A087784 A071224 A098660 this_sequence A034458 A067001 A057343
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KEYWORD
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sign
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AUTHOR
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Gary Adamson and Roger Bagula (qntmpkt(AT)yahoo.com), Oct 17 2006
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EXTENSIONS
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Edited by njas, Oct 29 2006
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