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A008500
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6-dimensional centered tetrahedral numbers.
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2
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1, 8, 36, 120, 330, 792, 1716, 3431, 6427, 11404, 19328, 31494, 49596, 75804, 112848, 164109, 233717, 326656, 448876, 607412, 810510, 1067760, 1390236, 1790643, 2283471, 2885156, 3614248, 4491586, 5540480, 6786900, 8259672
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OFFSET
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0,2
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COMMENTS
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If X is an n-set and Y a fixed 7-subset of X then a(n-7) is equal to the number of 7-subsets of X intersecting Y. - Milan Janjic, Jul 30 2007
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Milan Janjic, Two Enumerative Functions
Index to sequences with linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1)
Index entries for two-way infinite sequences
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FORMULA
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Expansion of (1-x^7)/(1-x)^8 = ( -1-x-x^2-x^3-x^4-x^5-x^6 ) / (x-1)^7.
G.f.: (1-x^7)/(1-x)^8. a(-1-n)=a(n).
720*a(n) = 720+1764*n+735*n^3+2128*n^2+385*n^4+21*n^5+7*n^6. - R. J. Mathar, Mar 14 2011
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PROG
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(PARI) a(n)=binomial(n+7, 7)-binomial(n, 7)
(MAGMA) [(720 + 1764*n +735*n^3 +2128*n^2 +385*n^4 +21*n^5 + 7*n^6)/720: n in [0..30]]; // Vincenzo Librandi, Oct 08 2011
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CROSSREFS
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Partial sums of A008489.
Sequence in context: A014343 A162596 A051192 * A008490 A023033 A000580
Adjacent sequences: A008497 A008498 A008499 * A008501 A008502 A008503
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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