A003878 a(n) = n^4 + (9/2)*n^3 + n^2 - (9/2)*n + 1.

1, 3, 48, 199, 543, 1191, 2278, 3963, 6429, 9883, 14556, 20703, 28603, 38559, 50898, 65971, 84153, 105843, 131464, 161463, 196311, 236503, 282558, 335019, 394453, 461451, 536628, 620623, 714099, 817743, 932266, 1058403, 1196913, 1348579, 1514208, 1694631

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A075681.

Programs

Magma

[(2*n^4+9*n^3+2*n^2-9*n+2)/2: n in [0..40]]; // G. C. Greubel, Jan 03 2024

Mathematica

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

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

Formula

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]

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

Extensions

Offset corrected by G. C. Greubel, Jan 03 2024