A335694 a(n) = 3*binomial(n,4) - 6*binomial(n,3) + 4*binomial(n,2) - 2.

-2, -2, 2, 4, 1, -7, -17, -23, -16, 16, 88, 218, 427, 739, 1181, 1783, 2578, 3602, 4894, 6496, 8453, 10813, 13627, 16949, 20836, 25348, 30548, 36502, 43279, 50951, 59593, 69283, 80102, 92134, 105466, 120188, 136393, 154177, 173639, 194881, 218008, 243128, 270352, 299794, 331571, 365803, 402613, 442127, 484474, 529786

Offset

0,1

References

I. Kaplansky and J. Riordan, The problème des ménages, Scripta Math. 12, (1946), 113-124. See p. 123.

Links

Table of n, a(n) for n=0..49.

I. Kaplansky and J. Riordan, The problème des ménages, Scripta Math. 12, (1946), 113-124. [Scan of annotated copy]

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

From Chai Wah Wu, Jul 20 2020: (Start)

a(n) = (n^4 - 14*n^3 + 51*n^2 - 38*n - 16)/8.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 4.

G.f.: (-11*x^4 + 6*x^3 + 8*x^2 - 8*x + 2)/(x - 1)^5. (End)

Prog

(PARI) a(n)=(n^4-14*n^3+51*n^2-38*n-16)/8 \\ Charles R Greathouse IV, Oct 21 2022

Crossrefs

Cf. A000179.

Sequence in context: A197116 A104461 A308042 * A084862 A327987 A216650

Adjacent sequences: A335691 A335692 A335693 * A335695 A335696 A335697

Keyword

sign,easy

Author

N. J. A. Sloane, Jul 20 2020

Status

approved