A017054 a(n) = (7*n + 6)^2.

36, 169, 400, 729, 1156, 1681, 2304, 3025, 3844, 4761, 5776, 6889, 8100, 9409, 10816, 12321, 13924, 15625, 17424, 19321, 21316, 23409, 25600, 27889, 30276, 32761, 35344, 38025, 40804, 43681, 46656

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

If Y is a fixed 2-subset of a (7n+1)-set X then a(n-1) is the number of 3-subsets of X intersecting Y. - Milan Janjic, Oct 21 2007

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Milan Janjic, Two Enumerative Functions
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A017053 (7*n+6).

Programs

Magma

[(7*n+6)^2: n in [0..40]]; // Vincenzo Librandi, Jul 10 2011

Mathematica

(7*Range[0,30]+6)^2 (* or *) LinearRecurrence[{3,-3,1},{36,169,400},40] (* Harvey P. Dale, Apr 28 2016 *)

PARI

a(n)=(7*n+6)^2 \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(0)=36, a(1)=169, a(2)=400. - Harvey P. Dale, Apr 28 2016

Sum_{n>=0} 1/a(n) = psi'(6/7)/49 = 0.04223032499681527770... - R. J. Mathar, May 07 2024

G.f.: -(36+61*x+x^2)/(x-1)^3 . - R. J. Mathar, May 07 2024