cp's OEIS Frontend

A075690 a(n) = (n-1)*(n-2)^4 - A028294(n), for n > 4, with a(1) = a(2) = 0, a(3) = 2, and a(4) = 48.

%I A075690 #13 Jan 03 2024 06:48:32
%S A075690 0,0,2,48,304,999,2393,4791,8542,14039,21719,32063,45596,62887,84549,
%T A075690 111239,143658,182551,228707,282959,346184,419303,503281,599127,
%U A075690 707894,830679,968623,1122911,1294772,1485479,1696349,1928743,2184066,2463767
%N A075690 a(n) = (n-1)*(n-2)^4 - A028294(n), for n > 4, with a(1) = a(2) = 0, a(3) = 2, and a(4) = 48.
%H A075690 G. C. Greubel, <a href="/A075690/b075690.txt">Table of n, a(n) for n = 1..1000</a>
%H A075690 Ed Pegg Jr., <a href="http://www.mathpuzzle.com/pancakes.htm">Pancakes</a>
%H A075690 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A075690 From _G. C. Greubel_, Jan 03 2024: (Start)
%F A075690 a(n) = (n-1)*(n-2)^4 - A028294(n) + 46*[n=1] - 23*[n=2] - 9*[n=3] + [n=4].
%F A075690 a(n) = (11*n^4 + 19*n^3 - 632*n^2 + 2012*n - 1686)/6 + 46*[n=1] - 23*[n=2] - 9*[n=3] + [n=4].
%F A075690 G.f.: x^3*(2 + 38*x + 84*x^2 - 61*x^3 - 32*x^4 + 14*x^5 - x^6)/(1-x)^5.
%F A075690 E.g.f.: (1/6)*(-1686 + 1410*x - 498*x^2 + 85*x^3 + 11*x^4)*exp(x) + 281 + 46*x - 23*x^2/2 - 9*x^3/3! + x^4/4!. (End)
%t A075690 LinearRecurrence[{5,-10,10,-5,1}, {0,0,2,48,304,999,2393,4791,8542}, 50] (* _G. C. Greubel_, Jan 03 2024 *)
%o A075690 (Magma) [0,0,2,48] cat [(11*n^4+19*n^3-632*n^2+2012*n-1686)/6: n in [4..50]]; // _G. C. Greubel_, Jan 03 2024
%o A075690 (SageMath) [0,0,2,48] + [(11*n^4+19*n^3-632*n^2+2012*n-1686)/6 for n in range(4,51)] # _G. C. Greubel_, Jan 03 2024
%Y A075690 Cf. A028294.
%K A075690 nonn
%O A075690 1,3
%A A075690 _Jon Perry_, Oct 12 2002
%E A075690 More terms from _David Wasserman_, Jan 22 2005
%E A075690 Name clarified by _G. C. Greubel_, Jan 03 2024