A016898 a(n) = (5*n + 4)^2.

16, 81, 196, 361, 576, 841, 1156, 1521, 1936, 2401, 2916, 3481, 4096, 4761, 5476, 6241, 7056, 7921, 8836, 9801, 10816, 11881, 12996, 14161, 15376, 16641, 17956, 19321, 20736, 22201, 23716, 25281, 26896, 28561, 30276, 32041, 33856, 35721, 37636, 39601, 41616

Offset

0,1

Comments

If Y is a fixed 2-subset of a (5n+1)-set X then a(n-1) is the number of 3-subsets of X intersecting Y. - Milan Janjic, Oct 21 2007

Interleaving of A017318 and A017378. - Michel Marcus, Aug 26 2015

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Milan Janjic, Two Enumerative Functions.

Eric Weisstein's MathWorld, Polygamma Function.

Wikipedia, Polygamma Function.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

From Colin Barker, Mar 30 2017: (Start)

G.f.: (16 + 33*x + x^2) / (1 - x)^3.

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

(End)

Sum_{n>=0} 1/a(n) = polygamma(1, 4/5)/25. - Amiram Eldar, Oct 02 2020

Example

a(0) = (5*0 + 4)^2 = 16.

Mathematica

Table[(5*n + 4)^2, {n, 0, 25}] (* Amiram Eldar, Oct 02 2020 *)
LinearRecurrence[{3, -3, 1}, {16, 81, 196}, 50] (* Harvey P. Dale, Jul 30 2023 *)

Prog

(Magma) [(5*n+4)^2: n in [0..70]]; // Vincenzo Librandi, May 02 2011
(PARI) Vec((16 + 33*x + x^2) / (1 - x)^3 + O(x^40)) \\ Colin Barker, Mar 30 2017

Crossrefs

Cf. A016850, A016862, A016874, A016886.

Sequence in context: A223951 A041490 A096020 * A224135 A265154 A268198

Adjacent sequences: A016895 A016896 A016897 * A016899 A016900 A016901

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved