A167471 Janet periodic table of the elements and structured hexagonal diamond numbers. a(n) = A166911(2*n) + A166911(2*n+1).

16, 128, 464, 1152, 2320, 4096, 6608, 9984, 14352, 19840, 26576, 34688, 44304, 55552, 68560, 83456, 100368, 119424, 140752, 164480, 190736, 219648, 251344, 285952, 323600, 364416, 408528, 456064, 507152, 561920, 620496, 683008, 749584, 820352, 895440, 974976

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = 16*n*(2 - 3*n + 4*n^2)/3 = 16*A100178(n).

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4), a(1)=16, a(2)=128, a(3)=464, a(4)=1152.

From Elmo R. Oliveira, Aug 28 2025: (Start)

G.f.: 16*x*(1 + 4*x + 3*x^2)/(1 - x)^4.

E.g.f.: 16*x*(3 + 9*x + 4*x^2)*exp(x)/3.

a(n) = A019558(n)/3. (End)

Mathematica

Table[16*n*(2 - 3*n + 4*n^2)/3, {n, 1, 50}] (* G. C. Greubel, Jun 13 2016 *)

Prog

(Magma) [16*n*(2-3*n+4*n^2)/3: n in [1..40]]; // Vincenzo Librandi, Aug 03 2011

Crossrefs

Cf. A019558, A100178, A166464, A166911.

Sequence in context: A367070 A291460 A004017 * A153115 A138331 A290031

Adjacent sequences: A167468 A167469 A167470 * A167472 A167473 A167474

Keyword

nonn,easy

Author

Paul Curtz, Nov 04 2009

Status

approved