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A064282
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Triangle with a(n,k)=C(3n+3,k)*(n-k+1)/(n+1).
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1
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1, 1, 3, 1, 6, 12, 1, 9, 33, 55, 1, 12, 63, 182, 273, 1, 15, 102, 408, 1020, 1428, 1, 18, 150, 760, 2565, 5814, 7752, 1, 21, 207, 1265, 5313, 15939, 33649, 43263, 1, 24, 273, 1950, 9750, 35880, 98670, 197340, 246675, 1, 27, 348, 2842, 16443, 71253, 237510
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OFFSET
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0,3
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,1000
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FORMULA
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a(n, k)=a(n-1, k)+3*a(n-1, k-1)+3*a(n-1, k-2)+a(n-1, k-3) [starting with a(0, 0)=1 and a(n, k)=0 if n<0 or n<k].
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PROG
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(PARI) { n=-1; for (m=0, 10^9, for (k=0, m, a=binomial(3*m + 3, k)*(m - k + 1)/(m + 1); write("b064282.txt", n++, " ", a); if (n==1000, break)); if (n==1000, break) ) } [From Harry J. Smith, Sep 11 2009]
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CROSSREFS
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Columns include A000012 and A008585. Right hand columns include A001764 and A006630. Row sums are A047099. Triangles A010054 (Triangle Indicator), A007318 (Pascal) and A050166 form a sequence which has this as its next member.
Sequence in context: A084536 A110770 A106855 * A087644 A049964 A143984
Adjacent sequences: A064279 A064280 A064281 * A064283 A064284 A064285
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KEYWORD
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nonn,tabl
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AUTHOR
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Henry Bottomley, Sep 24 2001
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STATUS
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approved
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