A100156 Structured truncated tetrahedral numbers.

1, 12, 44, 108, 215, 376, 602, 904, 1293, 1780, 2376, 3092, 3939, 4928, 6070, 7376, 8857, 10524, 12388, 14460, 16751, 19272, 22034, 25048, 28325, 31876, 35712, 39844, 44283, 49040, 54126, 59552, 65329, 71468, 77980, 84876, 92167, 99864, 107978, 116520, 125501, 134932

Offset: 1

Author

James A. Record (james.record(AT)gmail.com), Nov 07 2004

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..5000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A100155, A100157 for adjacent structured Archimedean solids; A100145 for more on structured polyhedral numbers. Similar to truncated tetrahedral numbers A005906.

Programs

Magma

[(1/6)*(11*n^3-3*n^2-2*n): n in [1..40]]; // Vincenzo Librandi, Jul 19 2011

Mathematica

Table[(11n^3-3n^2-2n)/6,{n,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{1,12,44,108},40] (* Harvey P. Dale, Sep 28 2011 *)

PARI

vector(50, n, (11*n^3 - 3*n^2 - 2*n)/6) \\ G. C. Greubel, Oct 18 2018

Formula

a(n) = (1/6)*(11*n^3 - 3*n^2 - 2*n).

From Harvey P. Dale, Sep 28 2011: (Start)

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(0)=1, a(1)=12, a(2)=44, a(3)=108.

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

E.g.f.: x*(6 + 30*x + 11*x^2)*exp(x)/6. - G. C. Greubel, Oct 18 2018