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

0,3

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).

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A244286 A223444 A084027 * A106212 A155022 A202639

Adjacent sequences: A063246 A063247 A063248 * A063250 A063251 A063252

Keyword

nonn,easy

Author

Henry Bottomley, Jul 11 2001

Status

approved