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Search: id:A158920
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| A158920 |
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Binomial trnasform of A008805 (triangular numbers with repeats). |
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1
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| 1, 2, 6, 16, 41, 102, 248, 592, 1392, 3232, 7424, 16896, 38144, 85504, 190464, 421888, 929792, 2039808, 4456448, 9699328, 21037056, 45481984, 98041856, 210763776, 451936256, 966787072, 2063597568, 4395630592, 9344909312, 19830669312
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OFFSET
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1,2
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FORMULA
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A007318 * (1, 1, 3, 3, 6, 6, 10, 10, 15, 15,...) = binomial transform of triangular numbers A000217 with repeats.
G.f.: x(x-1)^4/(1-2x)^3. a(n)=6*a(n-1)-12*a(n-2)+8*a(n-3), n>5. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 02 2009]
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EXAMPLE
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a(4) = 16 = (1, 3, 3, 1) dot (1, 1, 3, 3) = (1 + 3 + 9 + 3).
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MAPLE
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A000217 := proc(n) n*(n+1)/2 ; end: A008805 := proc(n) A000217( 1+floor(n/2) ) ; end: L := [seq(A008805(n), n=0..100)] ; read("transforms"); BINOMIAL(L) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 02 2009]
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CROSSREFS
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Cf. A008805
Sequence in context: A018021 A074405 A068786 this_sequence A143123 A152089 A102699
Adjacent sequences: A158917 A158918 A158919 this_sequence A158921 A158922 A158923
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 30 2009
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EXTENSIONS
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Extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 02 2009
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