A100152 Structured truncated cubic numbers.

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

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)/(1-x)^4. - Colin Barker, Jan 19 2012

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); 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^2-27n+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^3-27*n^2+2*n): n in [1..40]]; // Vincenzo Librandi, Jul 19 2011
(PARI) vector(50, n, (31*n^3-27*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