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A051937 Truncated triangular pyramid numbers: a(n) = Sum_{k=4..n} (k*(k+1)/2 - 9).

%I A051937 #45 Feb 17 2022 06:00:00
%S A051937 1,7,19,38,65,101,147,204,273,355,451,562,689,833,995,1176,1377,1599,
%T A051937 1843,2110,2401,2717,3059,3428,3825,4251,4707,5194,5713,6265,6851,
%U A051937 7472,8129,8823,9555,10326,11137,11989,12883,13820,14801,15827,16899,18018
%N A051937 Truncated triangular pyramid numbers: a(n) = Sum_{k=4..n} (k*(k+1)/2 - 9).
%C A051937 Binomial transform of [1, 6, 6, 1, 0, 0, 0, ...]. - _Gary W. Adamson_, Oct 22 2007
%H A051937 Vincenzo Librandi, <a href="/A051937/b051937.txt">Table of n, a(n) for n = 4..5000</a>
%H A051937 Milan Janjic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Janjic/janjic73.html">Binomial Coefficients and Enumeration of Restricted Words</a>, Journal of Integer Sequences, 2016, Vol 19, #16.7.3.
%H A051937 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A051937 a(n) = (1/6)*(n-3)*(n^2+6*n-34).
%F A051937 G.f.: x^4*(1+3*x-3*x^2)/(1-x)^4. - _Colin Barker_, Mar 19 2012
%F A051937 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - _Vincenzo Librandi_, Apr 28 2012
%F A051937 a(n) = A000290(n-4) + A005286(n-4). - _Ivan N. Ianakiev_, Dec 24 2019
%t A051937 CoefficientList[Series[(1+3*x-3*x^2)/(1-x)^4,{x,0,50}],x] (* _Vincenzo Librandi_, Apr 28 2012 *)
%t A051937 LinearRecurrence[{4,-6,4,-1},{1,7,19,38},50] (* _Harvey P. Dale_, Aug 12 2012 *)
%o A051937 (Magma) I:=[1, 7, 19, 38]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..45]]; // _Vincenzo Librandi_, Apr 28 2012
%o A051937 (PARI) a(n)=(n-3)*(n^2+6*n-34)/6 \\ _Charles R Greathouse IV_, Nov 10 2015
%Y A051937 Cf. A000292.
%K A051937 easy,nice,nonn
%O A051937 4,2
%A A051937 Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 21 1999