

A100156


Structured truncated tetrahedral numbers.


3



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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(n1)  6*a(n2) + 4*a(n3)  a(n4); a(0)=1, a(1)=12, a(2)=44, a(3)=108.
G.f.: x*(2*x*(x+4)+1)/(x1)^4. (End)
E.g.f.: x*(6 + 30*x + 11*x^2)*exp(x)/6.  G. C. Greubel, Oct 18 2018


MATHEMATICA

Table[(11n^33n^22n)/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^33*n^22*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: A106808 A296181 A007899 * 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



