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A077930
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Expansion of (1-x)^(-1)/(1+2*x+x^2+x^3).
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4
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1, -1, 2, -3, 6, -10, 18, -31, 55, -96, 169, -296, 520, -912, 1601, -2809, 4930, -8651, 15182, -26642, 46754, -82047, 143983, -252672, 443409, -778128, 1365520, -2396320, 4205249, -7379697, 12950466, -22726483, 39882198, -69988378, 122821042, -215535903, 378239143, -663763424
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (-1,1,0,1).
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FORMULA
| Unsigned version has g.f. 1/(1-x-x^2-x^4), with a(n)=a(n-1)+a(n-2)+a(n-4), a(n)=sum{k=0..floor(n/2), sum{i=0..n-k, C(i, n-k-i)C(2i-n+k, 3k-2n+2i)}}. Unsigned sequence gives diagonal sums of A038137. - Paul Barry (pbarry(AT)wit.ie), Oct 24 2005
Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 28 2010: (Start)
Unsigned = the INVERT transform of the aerated Fibonacci sequence:
(1, 0, 1, 0, 2, 0, 3, 0, 5,...). (End)
a(n+1)-a(n) = (-1)^(n+1)*A005314(n+2). - R. J. Mathar, Mar 14 2011
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CROSSREFS
| Signed version of A060945.
Sequence in context: A102702 A060945 A181532 * A023359 A082482 A066000
Adjacent sequences: A077927 A077928 A077929 * A077931 A077932 A077933
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KEYWORD
| sign
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 17 2002
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