A063249 Doubly hexagonal numbers.

0, 1, 66, 435, 1540, 4005, 8646, 16471, 28680, 46665, 72010, 106491, 152076, 210925, 285390, 378015, 491536, 628881, 793170, 987715, 1216020, 1481781, 1788886, 2141415, 2543640, 3000025, 3515226, 4094091, 4741660, 5463165

Offset: 0

Author

Henry Bottomley, Jul 11 2001

Keywords

• nonn
• easy

Examples

			a(2)=66 since 6 is the 2nd hexagonal number and 66 is the 6th hexagonal number.
		

Links

• William A. Tedeschi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A002817 for doubly triangular numbers, A000583 for doubly square numbers and A232713 for doubly pentagonal numbers.

Programs

Mathematica

LinearRecurrence[{5,-10,10,-5,1},{0,1,66,435,1540},30] (* Harvey P. Dale, Dec 02 2016 *)

PARI

concat(0, Vec(-x*(15*x^3+115*x^2+61*x+1)/(x-1)^5 + O(x^100))) \\ Colin Barker, Sep 14 2014

Formula

a(n) = n*(2*n-1)(4*n^2-2*n-1) = A000384(A000384(n)).

G.f.: -x*(15*x^3+115*x^2+61*x+1) / (x-1)^5. - Colin Barker, Sep 14 2014