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

Offset

1,2

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).

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

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 *)

Prog

(Magma) [(1/6)*(11*n^3-3*n^2-2*n): n in [1..40]]; // Vincenzo Librandi, Jul 19 2011
(PARI) vector(50, n, (11*n^3 - 3*n^2 - 2*n)/6) \\ G. C. Greubel, Oct 18 2018

Crossrefs

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

Sequence in context: A007899 A343729 A356322 * A320998 A294521 A309817

Adjacent sequences: A100153 A100154 A100155 * A100157 A100158 A100159

Keyword

easy,nonn

Author

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

Status

approved