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Search: id:A128099
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| A128099 |
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Triangle read by rows: T(n,k) is the number of ways to tile a 3 X n rectangle with k pieces of 2 X 2 tiles and 3n-4k pieces of 1 X 1 tiles (0<=k<=floor(n/2)). |
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+0
2
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| 1, 1, 1, 2, 1, 4, 1, 6, 4, 1, 8, 12, 1, 10, 24, 8, 1, 12, 40, 32, 1, 14, 60, 80, 16, 1, 16, 84, 160, 80, 1, 18, 112, 280, 240, 32, 1, 20, 144, 448, 560, 192, 1, 22, 180, 672, 1120, 672, 64, 1, 24, 220, 960, 2016, 1792, 448, 1, 26, 264, 1320, 3360, 4032, 1792, 128, 1, 28
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Row sums are the Jacobsthal numbers (A001045). Sum(k(T(n,k),k=0..floor(n/2))=A095977(n-1).
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FORMULA
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T(n,k)=2^k*binom(n-k,k). G.f.=1/(1-z-2tz^2).
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EXAMPLE
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Triangle starts:
1;
1;
1,2;
1,4;
1,6,4;
1,8,12;
1,10,24,8;
1,12,40,32;
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MAPLE
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T:=proc(n, k) if k<=n/2 then 2^k*binomial(n-k, k) else 0 fi end: for n from 0 to 16 do seq(T(n, k), k=0..floor(n/2)) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A001045, A095977.
Sequence in context: A146938 A147418 A146386 this_sequence A108952 A088522 A115124
Adjacent sequences: A128096 A128097 A128098 this_sequence A128100 A128101 A128102
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KEYWORD
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nonn,tabf
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 18 2007
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