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A077939
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Expansion of 1/(1-2*x-x^2-x^3).
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8
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1, 2, 5, 13, 33, 84, 214, 545, 1388, 3535, 9003, 22929, 58396, 148724, 378773, 964666, 2456829, 6257097, 15935689, 40585304, 103363394, 263247781, 670444260, 1707499695, 4348691431, 11075326817, 28206844760, 71837707768, 182957587113, 465959726754
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (2,1,1)
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FORMULA
| a(n) = abs(A077986(n)) = A077849(n)-A077849(n-1) = |A077922(n)|+|A077922(n-1)| = sum(k=0, n, A077997(k)). - Ralf Stephan, Feb 02 2004
a(n)=sum(m=1..n+1, sum(k=0..n-m+1, (sum(j=0..k, binomial(j,n-m-3*k+2*j+1)*binomial(k,j)))* binomial(m+k-1,m-1))). [From Vladimir Kruchinin, Oct 11 2011]
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MATHEMATICA
| CoefficientList[Series[1/(1-2*x-x^2-x^3), {x, 0, 40}], x] (* or *) LinearRecurrence[{2, 1, 1}, {1, 2, 5}, 40] (* From Vladimir Joseph Stephan Orlovsky, Jan 30 2012 *)
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PROG
| (Maxima)
a(n):=sum(sum((sum(binomial(j, n-m-3*k+2*j+1)*binomial(k, j), j, 0, k))* binomial(m+k-1, m-1), k, 0, n-m+1), m, 1, n+1); [From Vladimir Kruchinin, Oct 11 2011]
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CROSSREFS
| Sequence in context: A120925 A086588 * A077986 A007020 A080888 A052988
Adjacent sequences: A077936 A077937 A077938 * A077940 A077941 A077942
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 17 2002
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