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A012781 Take every 5th term of Padovan sequence A000931, beginning with the second term. 5
0, 1, 4, 16, 65, 265, 1081, 4410, 17991, 73396, 299426, 1221537, 4983377, 20330163, 82938844, 338356945, 1380359512, 5631308624, 22973462017, 93722435101, 382349636061, 1559831901918, 6363483400447, 25960439030624 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Number of nonisomorphic graded posets with 0 and uniform hasse graph of rank n, with exactly 2 elements of each rank level above 0, for n > 0. (Uniform used in the sense of Retakh, Serconek and Wilson.)  Here, we do not assume all maximal elements have maximal rank and thus use graded poset to mean: For every element x, all maximal chains among those with x as greatest element have the same finite length. - David Nacin, Feb 13 2012

REFERENCES

R. Stanley, Enumerative combinatorics, Vol. 1, Cambridge University Press, Cambridge, 1997, pp. 96-100.

LINKS

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

V. Retakh, S. Serconek, and R. Wilson, Hilbert Series of Algebras Associated to Directed Graphs and Order Homology, arXiv:1010.6295 [math.RA], 2010-2011.

Index entries for linear recurrences with constant coefficients, signature (5,-4,1).

FORMULA

a(n+3) = 5*a(n+2) - 4*a(n+1) + a(n).

G.f.: x*(1-x)/(1-5*x+4*x^2-x^3). - Colin Barker, Feb 03 2012

MATHEMATICA

LinearRecurrence[{5, -4, 1}, {0, 1, 4}, 25] (* Harvey P. Dale, Jan 10 2012 *)

PROG

(MAGMA) I:=[0, 1, 4 ]; [n le 3 select I[n] else 5*Self(n-1)-4*Self(n-2)+Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 03 2012

(Python)

def a(n, adict={0:0, 1:1, 2:4}):

.if n in adict:

..return adict[n]

.adict[n]=5*a(n-1) - 4*a(n-2) + a(n-3)

.return adict[n] # David Nacin, Feb 27 2012

CROSSREFS

Sequence in context: A181879 A243872 A052927 * A132820 A165201 A026674

Adjacent sequences:  A012778 A012779 A012780 * A012782 A012783 A012784

KEYWORD

nonn,easy,changed

AUTHOR

N. J. A. Sloane

EXTENSIONS

Initial term 0 added by Colin Barker, Feb 03 2012

STATUS

approved

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Last modified October 15 07:38 EDT 2019. Contains 328026 sequences. (Running on oeis4.)