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A073044
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Triangle read by rows: T(n,k) (n>=1, k>=0) = number of n-sequences of 0's and 1's with no pair of adjacent 0's and exactly k pairs of adjacent 1's.
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1
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2, 2, 1, 2, 2, 1, 2, 3, 2, 1, 2, 4, 4, 2, 1, 2, 5, 6, 5, 2, 1, 2, 6, 9, 8, 6, 2, 1, 2, 7, 12, 14, 10, 7, 2, 1, 2, 8, 16, 20, 20, 12, 8, 2, 1, 2, 9, 20, 30, 30, 27, 14, 9, 2, 1, 2, 10, 25, 40, 50, 42, 35, 16, 10, 2, 1, 2, 11, 30, 55, 70, 77, 56, 44, 18, 11, 2, 1, 2, 12, 36, 70, 105, 112, 112, 72
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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REFERENCES
| S. J. Cyvin and I. Gutman, Kekule structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see pp. 67-68).
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FORMULA
| Recurrence: T(n, k)=T(n-1, k-1)+T(n-2, k).
G.f.=G(t, z)=z(2+2z-tz)/(1-tz-z^2). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 01 2005
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EXAMPLE
| T(5,2)=4 because the sequences of length 5 with 2 pairs 11 are 11101, 11011,10111, 01110.
Triangle starts:
2;
2,1;
2,2,1;
2,3,2,1;
2,4,4,2,1;
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MAPLE
| G:=z*(2+2*z-t*z)/(1-t*z-z^2):Gser:=simplify(series(G, z=0, 17)):for n from 1 to 15 do P[n]:=sort(coeff(Gser, z^n)) od:for n from 1 to 13 do seq(coeff(t*P[n], t^k), k=1..n) od; # yields sequence in triangular form
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CROSSREFS
| Row sums are the Fibonacci numbers (A000045).
Sequence in context: A160384 A178305 A024327 * A124800 A069163 A025260
Adjacent sequences: A073041 A073042 A073043 * A073045 A073046 A073047
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KEYWORD
| nonn,tabl
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AUTHOR
| Roger Cuculiere (cuculier(AT)imaginet.fr), Aug 24 2002
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 01 2005
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