A118375 Minimum over all permutations b of 1..n of sum b(i)*b^{-1}(i).

1, 5, 11, 20, 35, 57, 85, 120, 165, 221, 287, 364, 455, 561, 681, 816, 969, 1141, 1331, 1540, 1771, 2025, 2301, 2600, 2925, 3277, 3655, 4060, 4495, 4961, 5457, 5984, 6545, 7141, 7771, 8436, 9139, 9881, 10661, 11480, 12341, 13245, 14191, 15180, 16215

Offset

1,2

Comments

The maximum obtainable is A000330, the square pyramidal numbers. Problem suggested by Leroy Quet.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

sci.math thread.

Index entries for linear recurrences with constant coefficients, signature (4,-7,8,-7,4,-1).

Formula

a(n) = T(n) + e(n), where T(n) = n(n+1)(n+2)/6 = A000292(n) is the tetrahedral numbers and e(n) = 0 if n = 0,1 (mod 4) and 1 if n = 2,3 (mod 4). (Published by Rob Johnson in sci.math.)

G.f.: x*(1+2*x-x^2)*(1-x+x^2)/((1-x)^4*(1+x^2)). [Colin Barker, Apr 30 2012]

a(n) = 4*a(n-1) -7*a(n-2) +8*a(n-3) -7*a(n-4) +4*a(n-5) -a(n-6). - Vincenzo Librandi, Jun 27 2012

Mathematica

CoefficientList[Series[(1+2*x-x^2)*(1-x+x^2)/((1-x)^4*(1+x^2)), {x, 0, 50}], x]  (* Vincenzo Librandi, Jun 27 2012 *)

Prog

(Magma) I:=[1, 5, 11, 20, 35, 57]; [n le 6 select I[n] else 4*Self(n-1)-7*Self(n-2)+8*Self(n-3)-7*Self(n-4)+4*Self(n-5)-Self(n-6): n in [1..50]]; // Vincenzo Librandi, Jun 27 2012

Crossrefs

Cf. A000292, A000330.

Sequence in context: A212978 A026038 A080957 * A225376 A099400 A139534

Adjacent sequences: A118372 A118373 A118374 * A118376 A118377 A118378

Keyword

nonn,easy

Author

Franklin T. Adams-Watters, May 15 2006

Status

approved