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A133263
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Binomial transform of (1, 2, 0, 1, -1, 1, -1, 1,...).
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2
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 27 2010: (Start)
(1 + x^2 + x^3 + x^4 + ...)*(1 + x + 2x^2 + 3x^3 + 4x^4 + ...) =
(1 + x + 3x^2 + 5x^3 + 8x^4 + 12x^5 + ...). (End)
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LINKS
| Harvey P. Dale, Table of n, a(n) for n = 0..1000
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FORMULA
| A007318 * [1, 2, 0, 1, -1, 1, -1, 1,...]. Left column of A134249
a(n)=(n^2 + n + 4)/2 G.f.=(1-x^2+x^3)/(1-x)^3. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 12 2007
a(n)= A000124(n)+1, n>=1. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 12 2008
a(1)=1, a(2)=3; for n>=3, a(n)=a(n-1)+n-1. - Philippe Lallouet (philip.lallouet(AT)orange.fr), May 27 2008\
a(0)=1, a(1)=3, a(2)=5, a(3)=8, a(n)=3*a(n-1)-3*a(n-2)+a(n-3) [From Harvey P. Dale, Feb 13 2012]
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EXAMPLE
| a(3) = 8 = (1, 3, 3, 1) dot (1, 2 0, 1) = (1 + 6 + 0 + 1).
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MAPLE
| 1, seq((n^2+n+4)*1/2, n=1..50); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 12 2007
a:=n->sum((stirling2(j+1, n)), j=0..n):seq(a(n)+1, n=0..50); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 12 2008
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MATHEMATICA
| i=-1; s=3; lst={Abs[i]}; Do[s+=n+i; If[s>2, AppendTo[lst, s]], {n, 0, 5!, 1}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 30 2008]
Join[{1}, Table[(n^2+n+4)/2, {n, 50}]] (* or *) Join[{1}, LinearRecurrence[ {3, -3, 1}, {3, 5, 8}, 50]] (* From Harvey P. Dale, Feb 13 2012 *)
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CROSSREFS
| Cf. A134249.
Sequence in context: A095173 A002579 A023544 * A038088 A018917 A167385
Adjacent sequences: A133260 A133261 A133262 * A133264 A133265 A133266
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KEYWORD
| nonn,changed
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 15 2007
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 12 2007
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