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A051941
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Truncated triangular pyramid numbers: a(n) = (n-7)*(n^2 + 10*n - 108)/6, n >= 8.
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1
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6, 21, 46, 82, 130, 191, 266, 356, 462, 585, 726, 886, 1066, 1267, 1490, 1736, 2006, 2301, 2622, 2970, 3346, 3751, 4186, 4652, 5150, 5681, 6246, 6846, 7482, 8155, 8866, 9616, 10406, 11237, 12110, 13026, 13986, 14991, 16042, 17140, 18286, 19481
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OFFSET
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8,1
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LINKS
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FORMULA
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a(n) = Sum_{k=8..n} k*(k+1)/2-30.
Binomial transform of [6, 15, 10, 1, 0, 0, 0, ...]. - Gary W. Adamson, Oct 22 2007
O.g.f.: -x^8*(-6 + 3*x + 2*x^2)/(-1+x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)
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MATHEMATICA
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LinearRecurrence[{4, -6, 4, -1}, {6, 21, 46, 82}, 50] (* Harvey P. Dale, Oct 20 2013 *)
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PROG
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(Magma) [(n-7)*(n^2+10*n-108)/6 : n in [8..70]]; // Wesley Ivan Hurt, Apr 20 2021
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CROSSREFS
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 21 1999
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STATUS
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approved
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