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Search: id:A089640
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| A089640 |
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Enumeration of partial sums of 1+[1,2]+[2,3]+[1,2]+[2,3]+... |
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+0
1
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| 1, 1, 1, 1, 3, 4, 4, 6, 11, 15, 18, 27, 43, 59, 78, 115, 172, 239, 330, 480, 698, 980, 1379, 1988, 2856, 4037, 5726, 8211, 11737, 16656, 23700, 33885, 48341, 68749, 97941, 139811, 199316, 283780, 404442, 576879, 822223, 1171318, 1669543, 2380423
(list; graph; listen)
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OFFSET
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1,5
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FORMULA
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a(n)=Sum{C(k, n-[(3n+2)/2]), k=0...n}, where C(n, k) is the usual binomial coefficient and [...] denotes the floor function. - John W. Layman (layman(AT)math.vt.edu), Jan 06 2004
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EXAMPLE
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a(6)=4 because we have 6=1+1+2+2=1+2+3=1+2+2+1=1+1+3+1.
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PROGRAM
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(PARI) { n=15; v=vector(n); for (i=1, n, v[i]=vector(2^(i-1))); v[1][1]=1; for (i=2, n, k=length(v[i-1]); for (j=1, k, v[i][j]=v[i-1][j]+i%2+1; v[i][j+k]=v[i-1][j]+i%2+2)); c=vector(n); for (i=1, n, for (j=1, 2^(i-1), if (v[i][j]<=n, c[v[i][j]]++))); c }
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CROSSREFS
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Sequence in context: A078490 A047877 A100692 this_sequence A086659 A008473 A069088
Adjacent sequences: A089637 A089638 A089639 this_sequence A089641 A089642 A089643
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KEYWORD
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nonn
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AUTHOR
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Jon Perry (perry(AT)globalnet.co.uk), Jan 01 2004
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EXTENSIONS
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Corrected and extended by John W. Layman (layman(AT)math.vt.edu), Jan 06 2004
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