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

Author

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

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A100151, A100153 for adjacent structured Archimedean solids; A100145 for more on structured polyhedral numbers. Similar to truncated cubic numbers A005912.

Programs

Magma

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

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 *)

PARI

vector(50, n, (31*n^3-27*n^2+2*n)/6) \\ G. C. Greubel, Oct 18 2018

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