A100150 Structured snub cubic numbers.

1, 24, 107, 288, 605, 1096, 1799, 2752, 3993, 5560, 7491, 9824, 12597, 15848, 19615, 23936, 28849, 34392, 40603, 47520, 55181, 63624, 72887, 83008, 94025, 105976, 118899, 132832, 147813, 163880, 181071, 199424, 218977, 239768, 261835, 285216, 309949, 336072

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)*(38*n^3 - 48*n^2 + 16*n).

G.f.: x*(1 + 20*x + 17*x^2)/(1-x)^4. - Colin Barker, Jan 19 2012

From Elmo R. Oliveira, Aug 05 2025: (Start)

E.g.f.: exp(x)*x*(19*x^2 + 33*x + 3)/3.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 4. (End)

Mathematica

LinearRecurrence[{4, -6, 4, -1}, {1, 24, 107, 288}, 40] (* Harvey P. Dale, Sep 17 2020 *)

Prog

(PARI) a(n)=n*(38*n^2-48*n+16)/6 \\ Charles R Greathouse IV, Jul 18 2011
(Magma) [(1/6)*(38*n^3-48*n^2+16*n): n in [1..40]]; // Vincenzo Librandi, Jul 19 2011

Crossrefs

Cf. A100149, A100151 for adjacent structured Archimedean solids; and A100145 for more on structured polyhedral numbers.

Sequence in context: A213874 A100149 A013980 * A305950 A060334 A271915

Adjacent sequences: A100147 A100148 A100149 * A100151 A100152 A100153

Keyword

nonn,easy

Author

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

Extensions

Deleted extra +16 in formula, corrected by Craig Ferguson, Jul 18 2011

Status

approved