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

1,2

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)*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)

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A100154 A246230 A100148 * A338109 A179811 A268805

Adjacent sequences: A100148 A100149 A100150 * A100152 A100153 A100154

Keyword

easy,nonn

Author

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

Status

approved