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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(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: 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

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Last modified November 26 15:30 EST 2020. Contains 338640 sequences. (Running on oeis4.)