A095934 Expansion of (1-x)^2/(1-5*x+3*x^2).

1, 3, 13, 56, 241, 1037, 4462, 19199, 82609, 355448, 1529413, 6580721, 28315366, 121834667, 524227237, 2255632184, 9705479209, 41760499493, 179686059838, 773148800711, 3326685824041, 14313982718072, 61589856118237, 265007332436969, 1140267093830134

Offset

0,2

Comments

a(n) is the number of generalized compositions of n when there are i+2 different types of i, (i=1,2,...). [Milan Janjic, Sep 24 2010]

Links

Table of n, a(n) for n=0..24.

P. J. Cameron, Some sequences of integers, Discrete Math., 75 (1989), 89-102.

P. J. Cameron, Some sequences of integers, in "Graph Theory and Combinatorics 1988", ed. B. Bollobas, Annals of Discrete Math., 43 (1989), 89-102.

Index entries for linear recurrences with constant coefficients, signature (5,-3).

Formula

a(n+2) = 5a(n+1) - 3a(n) (n >= 1); a(0) = 1, a(1) = 3, a(2) = 13.

Mathematica

CoefficientList[Series[(1-x)^2/(1-5x+3x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{5, -3}, {1, 3, 13}, 30] (* Harvey P. Dale, Jun 21 2021 *)

Prog

(PARI) a(n)=polcoeff((1-x)^2/(1-5*x+3*x^2)+x*O(x^n), n)

Crossrefs

Cf. A003480, A010903, A010920; equals A095939 + A095940.

Sequence in context: A234645 A010920 A010903 * A151220 A151221 A020515

Adjacent sequences: A095931 A095932 A095933 * A095935 A095936 A095937

Keyword

nonn,easy

Author

N. J. A. Sloane, Jul 13 2004

Status

approved