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

Offset: 1

Author

Paul Curtz, Nov 04 2009

Keywords

• nonn
• easy

Comments

(A166911=3,13,39,89,171,293,). 5 formulas for a(n):fifth is a(n)=4a(n-1)-6a(n-2)+4a(n-3)-a(n-4), a(0)=16,a(1)=128,a(2)=464,a(3)=1152. See A166464 and its companion A166911 (offset 0). Note, for a(n) mod 10, period 5:repeat 6,8,4,2,0. Mathematically, a(n) (then A100178=1,8,29,72,145,) can be preceded by 0.

Links

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

Programs

Magma

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

Mathematica

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

Formula

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