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A139545
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Binomial transform of [1, 0, 0, 4, 0, 0, 7, 0, 0, 10,...].
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0
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1, 1, 1, 5, 17, 41, 88, 190, 421, 935, 2051, 4445, 9562, 20476, 43681, 92837, 196613, 415073, 873820, 1835002, 3844765, 8039075, 16777223, 34952549, 72701278, 150994936, 313174681, 648719009, 1342177289, 2773833065, 5726623072
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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FORMULA
| A007318 * [1, 0, 0, 4, 0, 0, 7, 0, 0, 10,...].
a(n)=Sum((3k+1)binom(n,3k), k=0..n/3) - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 03 2008
G.f.: x(1-3x+3x^2+x^3)(1-x)^2/((1-2x)^2*(1-x+x^2)^2). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 25 2008]
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EXAMPLE
| a(4) = 5 = (1, 3, 3, 1) dot (1, 0, 0, 4) = (1 + 0 + 0 + 4).
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MAPLE
| a:=proc(n) options operator, arrow: sum((3*k+1)*binomial(n, 3*k), k=0..(1/3)*n) end proc: seq(a(n), n=0..30); - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 03 2008
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CROSSREFS
| Sequence in context: A109722 A097121 A007904 * A106972 A086499 A097123
Adjacent sequences: A139542 A139543 A139544 * A139546 A139547 A139548
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 26 2008
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), May 03 2008
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