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A123952
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Sum of first row of the 5 X 5 matrix M^n, where M={5,-1,0,0,0},{-1,5,-1,0,0},{0, -1,5,-1,0},{0,0,-1,5,-1},{0,0,0,-1,5}.
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1, 4, 17, 77, 371, 1891, 10123, 56503, 326699, 1945799, 11879987, 74039167, 469266331, 3014973511, 19581735203, 128267231663, 845770626539, 5605309590679, 37293554232307, 248855791875007, 1664285028373691
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| a(n)=25a(n-1)-246a(n-2)+1190a(n-3)-2828a(n-4)+2640a(n-5) (follows from the minimal polynomial of M).
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EXAMPLE
| a(2)=17 because the first row of M^2 is [26,-10,1,0,0].
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MAPLE
| with(linalg): M[1]:=matrix(5, 5, [5, -1, 0, 0, 0, -1, 5, -1, 0, 0, 0, -1, 5, -1, 0, 0, 0, -1, 5, -1, 0, 0, 0, -1, 5]): for n from 2 to 30 do M[n]:=multiply(M[1], M[n-1]) od: 1, seq(add(M[n][1, j], j=1..5), n=1..20);
a[0]:=1: a[1]:=4: a[2]:=17: a[3]:=77: a[4]:=371: for n from 5 to 20 do a[n]:=25*a[n-1]-246*a[n-2]+1190*a[n-3]-2828*a[n-4]+2640*a[n-5] od: seq(a[n], n=0..20);
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MATHEMATICA
| M = {{5, -1, 0, 0, 0}, {-1, 5, -1, 0, 0}, {0, -1, 5, -1, 0}, {0, 0, -1, 5, -1}, {0, 0, 0, -1, 5}}; v[1] = {1, 1, 1, 1, 1}; v[n_] := v[n] = M.v[n - 1]; a1 = Table[v[n][[1]], {n, 1, 50}]
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CROSSREFS
| Sequence in context: A124325 A151248 A104455 * A005494 A193782 A053486
Adjacent sequences: A123949 A123950 A123951 * A123953 A123954 A123955
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KEYWORD
| nonn
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AUTHOR
| Gary Adamson and Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 27 2006
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 24 2006
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