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
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Anthony G. Shannon, Hakan Akkuş, Yeşim Aküzüm, Ömür Deveci, and Engin Özkan, A partial recurrence Fibonacci link, Notes Num. Theor. Disc. Math. (2024) Vol. 30, No. 3, 530-537. See Table 2, p. 534.
- Index entries for linear recurrences with constant coefficients, signature (7,-17,17,-6).
Programs
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Magma
[(2*n +9 -2^(n+5) +3^(n+3))/4: n in [0..50]]; // G. C. Greubel, Jul 21 2022
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Mathematica
LinearRecurrence[{7,-17,17,-6}, {1,7,32,122}, 50] (* G. C. Greubel, Jul 21 2022 *) CoefficientList[Series[1/((1-x)^2(1-2x)(1-3x)),{x,0,30}],x] (* Harvey P. Dale, Feb 11 2025 *) -
SageMath
[(2*n+9 -2^(n+5) +3^(n+3))/4 for n in (0..50)] # G. C. Greubel, Jul 21 2022
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