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Search: id:A109526
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| A109526 |
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a(n)=the sum of the (1,2)- and (1,3)-entries and 2 times the (1,4)-entry of the matrix P^n + T^n, where the 4 X 4 matrices P and T are defined by P=[0,1,0,0;0,0,1,0;0,0,0,1;1,0,0,0] and T=[0,1,0,0;0,0,1,0;0,0,0,1;1,0,0,1]. |
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| 0, 2, 2, 4, 2, 4, 5, 8, 8, 12, 16, 23, 29, 41, 56, 78, 105, 146, 201, 278, 381, 527, 727, 1004, 1383, 1910, 2636, 3639, 5020, 6930, 9565, 13203, 18221, 25151, 34715, 47917, 66136, 91287, 126001, 173917, 240051, 331338, 457338, 631254, 871303, 1202641
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OFFSET
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0,2
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EXAMPLE
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a(7)=8 because P^7=[0,0,0,1;1,0,0,0;0,1,0,0;0,0,1,0], T^7=[1,1,1,2;2,1,1,3;3,2,1,4;4,3,2,5] and so P^7+T^7=[1,1,1,3;3,1,1,3;3,3,1,4;4,3,3,5] and now a(7)=1+1+2*3=8.
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MAPLE
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with(linalg): a:=proc(n) local P, T, k: P[1]:=matrix(4, 4, [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0]): T[1]:=matrix(4, 4, [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1]):for k from 2 to n do P[k]:=multiply(P[1], P[k-1]): T[k]:=multiply(T[1], T[k-1]) od: evalm(P[n]+T[n])[1, 2]+evalm(P[n]+T[n])[1, 3]+2*evalm(P[n]+T[n])[1, 4] end: 0, seq(a(n), n=1..50);
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MATHEMATICA
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v[0] = {0, 1, 1, 2}; w[0] = {0, 1, 1, 2}; M4 = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 0, 0}}; Mt = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 0, 1}}; v[n_] := v[n] = M4.v[n - 1] w[n_] := w[n] = Mt.w[n - 1] a = Table[(w[n] + v[n])[[1]], {n, 0, 50}]
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CROSSREFS
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Cf. A000045, A000213, A000931, A000078, A103632.
Sequence in context: A116467 A079314 A060609 this_sequence A059214 A091820 A140821
Adjacent sequences: A109523 A109524 A109525 this_sequence A109527 A109528 A109529
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 17 2005
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