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A133263
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Binomial transform of (1, 2, 0, 1, -1, 1, -1, 1, ...).
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6
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1, 3, 5, 8, 12, 17, 23, 30, 38, 47, 57, 68, 80, 93, 107, 122, 138, 155, 173, 192, 212, 233, 255, 278, 302, 327, 353, 380, 408, 437, 467, 498, 530, 563, 597, 632, 668, 705, 743, 782, 822, 863, 905, 948, 992, 1037, 1083, 1130, 1178, 1227, 1277
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = (n^2 + n + 4)/2 for n > 0.
G.f.: (1 - x^2 + x^3)/(1-x)^3. (End)
a(0)=1, a(1)=3; for n >= 2, a(n) = a(n-1) + n. - Philippe Lallouet (philip.lallouet(AT)orange.fr), May 27 2008; corrected by Michel Marcus, Nov 03 2018
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(0)=1, a(1)=3, a(2)=5, a(3)=8. - Harvey P. Dale, Feb 13 2012
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EXAMPLE
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a(3) = 8 = (1, 3, 3, 1) dot (1, 2 0, 1) = (1 + 6 + 0 + 1).
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MAPLE
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a:=n->add((Stirling2(j+1, n)), j=0..n): seq(a(n)+1, n=0..50); # Zerinvary Lajos, Apr 12 2008
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MATHEMATICA
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Join[{1}, Table[(n^2+n+4)/2, {n, 50}]] (* or *) Join[{1}, LinearRecurrence[ {3, -3, 1}, {3, 5, 8}, 50]] (* Harvey P. Dale, Feb 13 2012 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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