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A214825
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a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 3.
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49
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1, 3, 3, 7, 13, 23, 43, 79, 145, 267, 491, 903, 1661, 3055, 5619, 10335, 19009, 34963, 64307, 118279, 217549, 400135, 735963, 1353647, 2489745, 4579355, 8422747, 15491847, 28493949, 52408543, 96394339, 177296831, 326099713, 599790883, 1103187427
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OFFSET
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0,2
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COMMENTS
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Part of a group of sequences defined by a(0), a(1)=a(2), a(n) = a(n-1) + a(n-2) + a(n-3) which is a subgroup of sequences with linear recurrences and constant coefficients listed in the index. See Comments in A214727.
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LINKS
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FORMULA
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G.f.: (1+2*x-x^2)/(1-x-x^2-x^3).
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MATHEMATICA
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LinearRecurrence[{1, 1, 1}, {1, 3, 3}, 40] (* Harvey P. Dale, Oct 05 2013 *)
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PROG
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(PARI) my(x='x+O('x^40)); Vec((1+2*x-x^2)/(1-x-x^2-x^3)) \\ G. C. Greubel, Apr 23 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+2*x-x^2)/(1-x-x^2-x^3) )); // G. C. Greubel, Apr 23 2019
(SageMath) ((1+2*x-x^2)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 23 2019
(GAP) a:=[1, 3, 3];; for n in [4..40] do a[n]:=a[n-1]+a[n-2]+a[n-3]; od; a; # G. C. Greubel, Apr 23 2019
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CROSSREFS
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Cf. A000073, A000213, A000288, A000322, A000383, A001644, A060455, A136175, A141036, A141523, A214825-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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