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

Author

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

Keywords

• easy
• nonn

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

Programs

Magma

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

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)