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A108122
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G.f.: (1-2*x^2)/(1-x-2*x^2-x^3).
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0
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1, 1, 1, 4, 7, 16, 34, 73, 157, 337, 724, 1555, 3340, 7174, 15409, 33097, 71089, 152692, 327967, 704440, 1513066, 3249913, 6980485, 14993377, 32204260, 69171499, 148573396, 319120654
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| The sequence counts row lengths of an array in which rows are obtained by the substitution 1->2, 2->3, 3->1,2,2,3 from previous rows:
1;
2;
3;
1,2,2,3;
2,3,3,1,2,2,3;
3,1,2,2,3,1,2,2,3,2,3,3,1,2,2,3;
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients, signature (1,2,1).
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FORMULA
| a(n) = a(n-1) + 2*a(n-2) + a(n-3), starting 1,1,1.
a(n) = A002478(n) - 2*A002478(n-2), n>1.
a(n):=sum(m=0..n/2, sum(i=0..m, 2^i*binomial(n-2*m+1,m-i)*binomial(n-2*m+i,n-2*m))). [Vladimir Kruchinin, Dec 17 2011]
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MATHEMATICA
| s[1] = {2}; s[2] = {3}; s[3] = {1, 2, 2, 3}; t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]] a0 = Table[Length[p[i]], {i, 0, 20}]
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PROG
| (Maxima)
a(n):=sum(sum(2^i*binomial(n-2*m+1, m-i)*binomial(n-2*m+i, n-2*m), i, 0, m), m, 0, (n)/2); [Vladimir Kruchinin, Dec 17 2011]
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CROSSREFS
| Cf. A078007, A101399.
Sequence in context: A093210 A133600 A051049 * A192800 A027609 A145763
Adjacent sequences: A108119 A108120 A108121 * A108123 A108124 A108125
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KEYWORD
| nonn
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 04 2005
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