

A100152


Structured truncated cubic numbers.


3



1, 24, 100, 260, 535, 956, 1554, 2360, 3405, 4720, 6336, 8284, 10595, 13300, 16430, 20016, 24089, 28680, 33820, 39540, 45871, 52844, 60490, 68840, 77925, 87776, 98424, 109900, 122235, 135460, 149606, 164704
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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)*n*(31*n^2  27*n + 2).
G.f.: x*(1 + 20*x + 10*x^2)/(1x)^4.  Colin Barker, Jan 19 2012
a(n) = 4*a(n1)  6*a(n2) + 4*a(n3)  a(n4); a(1)=1, a(2)=24, a(3)=100, a(4)=260.  Harvey P. Dale, Jan 11 2016
E.g.f.: x*(6 + 66*x + 31*x^2)*exp(x)/6.  G. C. Greubel, Oct 18 2018


MATHEMATICA

Table[n/6 (31n^227n+2), {n, 40}] (* or *) LinearRecurrence[{4, 6, 4, 1}, {1, 24, 100, 260}, 40] (* Harvey P. Dale, Jan 11 2016 *)


PROG

(Magma) [(1/6)*(31*n^327*n^2+2*n): n in [1..40]]; // Vincenzo Librandi, Jul 19 2011
(PARI) vector(50, n, (31*n^327*n^2+2*n)/6) \\ G. C. Greubel, Oct 18 2018


CROSSREFS

Cf. A100151, A100153 for adjacent structured Archimedean solids; A100145 for more on structured polyhedral numbers. Similar to truncated cubic numbers A005912.
Sequence in context: A042124 A042126 A157514 * A233405 A297798 A048529
Adjacent sequences: A100149 A100150 A100151 * A100153 A100154 A100155


KEYWORD

nonn,easy


AUTHOR

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


STATUS

approved



