A100146 Structured great rhombicubeoctahedral numbers.

1, 48, 221, 600, 1265, 2296, 3773, 5776, 8385, 11680, 15741, 20648, 26481, 33320, 41245, 50336, 60673, 72336, 85405, 99960, 116081, 133848, 153341, 174640, 197825, 222976, 250173, 279496, 311025, 344840, 381021, 419648, 460801, 504560, 551005, 600216, 652273

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)*(80*n^3 - 102*n^2 + 28*n).

From Jaume Oliver Lafont, Sep 08 2009: (Start)

a(n) = ((n-1)+1)*(5*(n-1)+3)*(8*(n-1)+1)/3.

G.f.: x*(1 + 44*x + 35*x^2)/(1-x)^4. (End)

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

E.g.f.: exp(x)*x*(40*x^2 + 69*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, 48, 221, 600}, 40] (* Harvey P. Dale, Jan 07 2026 *)

Prog

(Magma) [((n-1)+1)*(5*(n-1)+3)*(8*(n-1)+1)/3: n in [1..40]]; // Vincenzo Librandi, Jul 19 2011

Crossrefs

Cf. A100145, A100147 for adjacent structured Archimedean solids; and A100145 for more on structured polyhedral numbers.

Sequence in context: A364922 A235759 A062248 * A235542 A269014 A265422

Adjacent sequences: A100143 A100144 A100145 * A100147 A100148 A100149

Keyword

easy,nonn

Author

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

Status

approved