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A187693 G.f.: x^2*(1+4*x-3*x^2)/((1-x)^2*(1-2*x)*(1-3*x)). 2
0, 0, 1, 11, 57, 229, 815, 2715, 8701, 27233, 83979, 256519, 778745, 2354637, 7100743, 21375923, 64275189, 193120441, 579951107, 1741032927, 5225458033, 15681092645, 47052715071, 141177019531, 423568807277, 1270781919249, 3812496752635, 11437792247735, 34313980722921, 102943150128253, 308831866303799, 926500430749539 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

F. Bergeron, M. Bousquet-Mélou and S. Dulucq, Standard paths in the composition poset, Ann. Sci. Math. Quebec, 19 (1995), no. 2, 139-151.

Index entries for linear recurrences with constant coefficients, signature (7,-17,17,-6).

FORMULA

a(n) = n + (7 + 3^(n+1) - 9*2^n)/2, n>0. - R. J. Mathar, Mar 18 2011

E.g.f.: (-1 + (7+2*x)*exp(x) - 9*exp(2*x) + 3*exp(3*x))/2. - G. C. Greubel, Nov 07 2018

MATHEMATICA

Join[{0}, LinearRecurrence[{7, -17, 17, -6}, {0, 1, 11, 57}, 50]] (* G. C. Greubel, Nov 07 2018 *)

PROG

(PARI) concat([0, 0], Vec(x^2*(1+4*x-3*x^2)/((1-x)^2*(1-2*x)*(1-3*x)) + O(x^40))) \\ Michel Marcus, Nov 07 2018

(MAGMA) I:=[0, 1, 11, 57]; [0] cat [n le 4 select I[n] else 7*Self(n-1) - 17*Self(n-2) +17*Self(n-3) -6*Self(n-4): n in [1..30]]; // G. C. Greubel, Nov 07 2018

CROSSREFS

Cf. A187693.

Sequence in context: A211614 A244497 A101094 * A200529 A289255 A275795

Adjacent sequences:  A187690 A187691 A187692 * A187694 A187695 A187696

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Mar 12 2011

STATUS

approved

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Last modified September 17 04:49 EDT 2019. Contains 327119 sequences. (Running on oeis4.)