A249999 Expansion of 1/((1-x)^2*(1-2*x)*(1-3*x)).

1, 7, 32, 122, 423, 1389, 4414, 13744, 42245, 128771, 390396, 1179366, 3554467, 10696153, 32153978, 96592988, 290041089, 870647535, 2612991160, 7841070610, 23527406111, 70590606917, 211788597942, 635399348232, 1906265153533, 5718929678299, 17157057470324, 51471709281854

Offset

0,2

Links

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

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

Formula

G.f.: 1/((1-x)^2 * (1-2*x) * (1-3*x)).

a(n) = 9/4 - 2^(n+3) + n/2 + 3^(n+3)/4. - R. J. Mathar, Jan 09 2015

E.g.f.: (1/4)*((9 + 2*x) - 32*exp(x) + 27*exp(2*x))*exp(x). - G. C. Greubel, Jul 21 2022

Mathematica

LinearRecurrence[{7, -17, 17, -6}, {1, 7, 32, 122}, 50] (* G. C. Greubel, Jul 21 2022 *)

Prog

(Magma) [(2*n +9 -2^(n+5) +3^(n+3))/4: n in [0..50]]; // G. C. Greubel, Jul 21 2022
(SageMath) [(2*n+9 -2^(n+5) +3^(n+3))/4 for n in (0..50)] # G. C. Greubel, Jul 21 2022

Crossrefs

Cf. A000392 (first differences), A094705, A243869, A249997.

Sequence in context: A133107 A178851 A213163 * A034360 A268745 A199845

Adjacent sequences: A249996 A249997 A249998 * A250000 A250001 A250002

Keyword

nonn,easy

Author

Alex Ratushnyak, Dec 28 2014

Status

approved