A000338 Expansion of x^3*(5-2*x)*(1-x^3)/(1-x)^4. (Formerly M3877 N1589)

5, 18, 42, 75, 117, 168, 228, 297, 375, 462, 558, 663, 777, 900, 1032, 1173, 1323, 1482, 1650, 1827, 2013, 2208, 2412, 2625, 2847, 3078, 3318, 3567, 3825, 4092, 4368, 4653, 4947, 5250, 5562, 5883, 6213, 6552, 6900, 7257, 7623, 7998, 8382, 8775, 9177, 9588, 10008, 10437, 10875, 11322, 11778

Offset

3,1

References

J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

Links

T. D. Noe, Table of n, a(n) for n = 3..1000

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992

J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23. [Annotated scanned copy]

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

Formula

a(n) = 3*A095794(n-2), n>3. - R. J. Mathar, May 30 2022

G.f.: (1+x+x^2)*(5-2*x)*x^3/(1-x)^3. - Simon Plouffe in his 1992 dissertation

Sum_{n>=3} 1/a(n) = log(3)/5 + Pi*sqrt(3)/45 = 0.3406424... - R. J. Mathar, Apr 22 2024

a(n) = 5*A005448(n-2) -2*A005448(n-3). - R. J. Mathar, Apr 22 2024

Maple

ff := n->9/2*n^2-15/2*n; seq(ff(n), n=3..60); # Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001, sequence without a(3).

Mathematica

nn = 100; CoefficientList[Series[(5 - 2 x) (1 - x^3)/(1 - x)^4, {x, 0, nn}], x] (* T. D. Noe, Jun 19 2012 *)
LinearRecurrence[{3, -3, 1}, {5, 18, 42, 75}, 60] (* Harvey P. Dale, Sep 20 2016 *)

Crossrefs

Sequence in context: A276819 A236364 A352368 * A212343 A056640 A272703

Adjacent sequences: A000335 A000336 A000337 * A000339 A000340 A000341

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Extensions

More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001

Status

approved