A100151 Structured snub dodecahedral numbers.

1, 60, 286, 788, 1675, 3056, 5040, 7736, 11253, 15700, 21186, 27820, 35711, 44968, 55700, 68016, 82025, 97836, 115558, 135300, 157171, 181280, 207736, 236648, 268125, 302276, 339210, 379036, 421863, 467800, 516956, 569440, 625361, 684828, 747950, 814836, 885595

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. A100150, A100152 for adjacent structured Archimedean solids; and A100145 for more on structured polyhedral numbers.

Programs

Magma

[(1/6)*(109*n^3-153*n^2+50*n): n in [1..40]]; // Vincenzo Librandi, Jul 19 2011

Mathematica

LinearRecurrence[{4, -6, 4, -1}, {1, 60, 286, 788}, 50] (* Paolo Xausa, Aug 06 2025 *)

Formula

a(n) = (1/6)*n*(109*n^2 - 153*n + 50).

G.f.: x*(1 + 56*x + 52*x^2)/(1-x)^4. - Colin Barker, Jan 19 2012

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

E.g.f.: exp(x)*x*(109*x^2 + 174*x + 6)/6.

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