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A214829
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a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 7.
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10
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1, 7, 7, 15, 29, 51, 95, 175, 321, 591, 1087, 1999, 3677, 6763, 12439, 22879, 42081, 77399, 142359, 261839, 481597, 885795, 1629231, 2996623, 5511649, 10137503, 18645775, 34294927, 63078205, 116018907, 213392039, 392489151, 721900097, 1327781287, 2442170535
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: (1+6*x-x^2)/(1-x-x^2-x^3).
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MATHEMATICA
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LinearRecurrence[{1, 1, 1}, {1, 7, 7}, 40] (* G. C. Greubel, Apr 24 2019 *)
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PROG
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(PARI) Vec((x^2-6*x-1)/(x^3+x^2+x-1) + O(x^40)) \\ Michel Marcus, Jun 04 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+6*x-x^2)/(1-x-x^2-x^3) )); // G. C. Greubel, Apr 24 2019
(Sage) ((1+6*x-x^2)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 24 2019
(GAP) a:=[1, 7, 7];; for n in [4..40] do a[n]:=a[n-1]+a[n-2]+a[n-3]; od; a; # G. C. Greubel, Apr 24 2019
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CROSSREFS
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Cf. A000213, A000288, A000322, A000383, A060455, A136175, A141036, A141523, A214825, A214826, A214827, A214828, A214830, A214831.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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