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%I #20 Feb 17 2022 00:55:11
%S 6,21,46,82,130,191,266,356,462,585,726,886,1066,1267,1490,1736,2006,
%T 2301,2622,2970,3346,3751,4186,4652,5150,5681,6246,6846,7482,8155,
%U 8866,9616,10406,11237,12110,13026,13986,14991,16042,17140,18286,19481
%N Truncated triangular pyramid numbers: a(n) = (n-7)*(n^2 + 10*n - 108)/6, n >= 8.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = Sum_{k=8..n} k*(k+1)/2-30.
%F Binomial transform of [6, 15, 10, 1, 0, 0, 0, ...]. - _Gary W. Adamson_, Oct 22 2007
%F From _R. J. Mathar_, May 17 2008: (Start)
%F O.g.f.: -x^8*(-6 + 3*x + 2*x^2)/(-1+x)^4.
%F a(n+1) - a(n) = A051940(n+1).
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)
%t LinearRecurrence[{4,-6,4,-1},{6,21,46,82},50] (* _Harvey P. Dale_, Oct 20 2013 *)
%o (PARI) a(n)=(n-7)*(n^2+10*n-108)/6 \\ _Charles R Greathouse IV_, Nov 10 2015
%o (Magma) [(n-7)*(n^2+10*n-108)/6 : n in [8..70]]; // _Wesley Ivan Hurt_, Apr 20 2021
%Y Cf. A000292.
%K easy,nice,nonn
%O 8,1
%A Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 21 1999
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