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A051939
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Truncated triangular pyramid numbers: a(n)=sum(k*(k+1)/2-18,k=6..n).
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0
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3, 13, 31, 58, 95, 143, 203, 276, 363, 465, 583, 718, 871, 1043, 1235, 1448, 1683, 1941, 2223, 2530, 2863, 3223, 3611, 4028, 4475, 4953, 5463, 6006, 6583, 7195, 7843, 8528, 9251, 10013, 10815, 11658, 12543, 13471, 14443, 15460, 16523, 17633, 18791
(list; graph; refs; listen; history; internal format)
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OFFSET
| 6,1
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FORMULA
| a(n)=1/6*(n-5)*(n^2+8*n-66)
Equals binomial transform of (3, 10, 8, 1, 0, 0, 0,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 03 2008
a(6)=3, a(7)=13, a(8)=31, a(9)=58, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)- a(n-4) [From Harvey P. Dale, Oct 22 2011]
G.f.: (-3*x^2+x+3)/(x-1)^4 [From Harvey P. Dale, Oct 22 2011]
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MATHEMATICA
| Table[1/6*(n - 5)*(n^2 + 8*n - 66), {n, 6, 60}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Mar 31 2006
LinearRecurrence[{4, -6, 4, -1}, {3, 13, 31, 58}, 60] (* From Harvey P. Dale, Oct 22 2011 *)
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CROSSREFS
| A000292.
Sequence in context: A179027 A145907 A054554 * A146728 A082709 A154833
Adjacent sequences: A051936 A051937 A051938 * A051940 A051941 A051942
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KEYWORD
| easy,nice,nonn
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AUTHOR
| Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 21 1999
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