login
a(n) = n^4 + (9/2)*n^3 + n^2 - (9/2)*n + 1.
3

%I #23 Jan 03 2024 15:32:03

%S 1,3,48,199,543,1191,2278,3963,6429,9883,14556,20703,28603,38559,

%T 50898,65971,84153,105843,131464,161463,196311,236503,282558,335019,

%U 394453,461451,536628,620623,714099,817743,932266,1058403,1196913,1348579,1514208,1694631

%N a(n) = n^4 + (9/2)*n^3 + n^2 - (9/2)*n + 1.

%C Old name was: "Number of stacks of n pikelets, distance 4 flips from a well-ordered stack".

%H G. C. Greubel, <a href="/A003878/b003878.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F G.f.: (1 - 2*x + 43*x^2 - 21*x^3 + 3*x^4)/(1-x)^5. [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009]

%F E.g.f.: (1/2)*(2 + 4*x + 43*x^2 + 21*x^3 + 2*x^4)*exp(x). - _G. C. Greubel_, Jan 03 2024

%t Table[n^4+(9/2)(n^3-n)+n^2+1,{n,0,30}] (* _Harvey P. Dale_, Dec 01 2020 *)

%o (Magma) [(2*n^4+9*n^3+2*n^2-9*n+2)/2: n in [0..40]]; // _G. C. Greubel_, Jan 03 2024

%o (SageMath) [(2*n^4+9*n^3+2*n^2-9*n+2)/2 for n in range(41)] # _G. C. Greubel_, Jan 03 2024

%Y Cf. A075681.

%K nonn

%O 0,2

%A _N. J. A. Sloane_

%E Offset corrected by _G. C. Greubel_, Jan 03 2024