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Search: id:A081144
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| A081144 |
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Starting at 1, four-fold convolution of A000400 (powers of 6). |
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2
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| 0, 0, 0, 1, 24, 360, 4320, 45360, 435456, 3919104, 33592320, 277136640, 2217093120, 17293326336, 132058128384, 990435962880, 7313988648960, 53287631585280, 383670947414016, 2733655500324864, 19296391766999040, 135074742368993280
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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With a different offset, number of n-permutations (n=4)of 7 objects: t, u, v, w, z, x, y with repetition allowed, containing exactly three u's. Example: a(4)=24 because we have uuut, uutu, utuu, tuuu, uuuv, uuvu, uvuu, vuuu, uuuw, uuwu, uwuu, wuuu, uuuz, uuzu, uzuu, zuuu, uuux, uuxu, uxuu, xuuu, uuuy, uuyu, uyuu, yuuu. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 03 2008
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FORMULA
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a(n)=24a(n-1)-216a(n-2)+864a(n-3)-1296a(n-4), a(0)=a(1)=a(2)=0, a(3)=1. a(n)=6^(n-3)C(n, 3) G.f. x^3/(1-6x)^4
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MAPLE
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seq(seq(binomial(i+2, j)*6^(i-1), j =i-1), i=-2..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 30 2007
seq(binomial(n+3, 3)*6^n, n=-3..18); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 03 2008
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CROSSREFS
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Cf. A081143, A081136.
Cf. A038255.
Adjacent sequences: A081141 A081142 A081143 this_sequence A081145 A081146 A081147
Sequence in context: A122813 A028245 A005546 this_sequence A126780 A052741 A046905
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Mar 08 2003
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