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A103632
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Expansion of (1-x+x^2)/(1-x-x^4).
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3
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1, 0, 1, 1, 2, 2, 3, 4, 6, 8, 11, 15, 21, 29, 40, 55, 76, 105, 145, 200, 276, 381, 526, 726, 1002, 1383, 1909, 2635, 3637, 5020, 6929, 9564, 13201, 18221, 25150, 34714, 47915, 66136, 91286, 126000, 173915, 240051, 331337, 457337, 631252, 871303, 1202640
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Diagonal sums of A103631.
The Kn11 sums, see A180662, of triangle A065941 equal the terms of this sequence without a(0) and a(1). [Johannes W. Meijer, Aug 11 2011]
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FORMULA
| G.f.: (1-x+x^2)/(1-x-x^4)
a(n) = a(n-1) + a(n-4) with a(0)=1, a(1)=0, a(2)=1 and a(3)=1.
a(n) = sum{k=0..floor(n/2), binomial(floor((2*n-3*k-1)/2), n-2*k)}
a(n) = A003269(n+1) - A003269(n-4), n>4.
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MAPLE
| A103632 := proc(n): add( binomial(floor((2*n-3*k-1)/2), n-2*k), k=0..floor(n/2)) end: seq(A103632(n), n=0..46); # [Johannes W. Meijer, Aug 11 2011]
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CROSSREFS
| Sequence in context: A089333 A098492 A173508 * A067859 A006207 A017912
Adjacent sequences: A103629 A103630 A103631 * A103633 A103634 A103635
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Feb 11 2005
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EXTENSIONS
| Formula corrected by Johannes W. Meijer, Aug 11 2011
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