A007589 Dodecahedral surface numbers: a(0)=0, a(1)=1, a(2)=20, thereafter 2*((3*n-7)^2 + 21). (Formerly M5083)

0, 1, 20, 50, 92, 170, 284, 434, 620, 842, 1100, 1394, 1724, 2090, 2492, 2930, 3404, 3914, 4460, 5042, 5660, 6314, 7004, 7730, 8492, 9290, 10124, 10994, 11900, 12842, 13820, 14834, 15884, 16970, 18092, 19250

Offset

0,3

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = Vertices + Edges*(n-2) + Faces*facenumber(n-3) = 20 + 30(n-2) + 12*A000326(n-3). - Mitch Harris, Oct 25 2006

From G. C. Greubel, Aug 30 2019: (Start)

G.f.: x*(1 + 17*x - 7*x^2 + x^3 + 24*x^4)/(1-x)^3.

E.g.f.: -140 -73*x -12*x^2 + (140 -66*x +18*x^2)*exp(x). (End)

Maple

seq(coeff(series(x*(1+17*x-7*x^2+x^3+24*x^4)/(1-x)^3, x, n+1), x, n), n = 0 .. 45); # G. C. Greubel, Aug 30 2019

Mathematica

Join[{0, 1, 20}, 2((3Range[3, 40]-7)^2+21)] (* Harvey P. Dale, Sep 24 2011 *)
Join[{0, 1, 20}, CoefficientList[Series[2*(25-29*x+22*x^2)/(1-x)^3, {x, 0, 50}], x] ] (* Vincenzo Librandi, Jul 07 2012 *)

Prog

(Magma) I:=[0, 1, 20, 50, 92, 170]; [n le 6 select I[n] else 3*Self(n-1) -3*Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Jul 07 2012
(PARI) my(x='x+O('x^45)); concat([0], Vec(x*(1+17*x-7*x^2+x^3+24*x^4)/(1-x)^3)) \\ G. C. Greubel, Aug 30 2019
(Sage)
def A007589_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P(x*(1+17*x-7*x^2+x^3+24*x^4)/(1-x)^3).list()
A007589_list(45) # G. C. Greubel, Aug 30 2019
(GAP) a:=[50, 92, 170];; for n in [4..45] do a[n]:=3*a[n-1]-3*a[n-2]+ a[n-3]; od; Concatenation([0, 1, 20], a); # G. C. Greubel, Aug 30 2019

Crossrefs

Sequence in context: A277553 A260093 A304832 * A182462 A231293 A227771

Adjacent sequences: A007586 A007587 A007588 * A007590 A007591 A007592

Keyword

nonn,easy,changed

Author

N. J. A. Sloane, R. K. Guy

Extensions

Revised definition from N. J. A. Sloane, Sep 25 2011

Status

approved