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A224785
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Expansion of (1+4*x+8*x^2-x^3)/((1-x)*(1+x)*(1-3*x^2)).
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1
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1, 4, 12, 15, 45, 48, 144, 147, 441, 444, 1332, 1335, 4005, 4008, 12024, 12027, 36081, 36084, 108252, 108255, 324765, 324768, 974304, 974307, 2922921, 2922924, 8768772, 8768775, 26306325, 26306328, 78918984, 78918987, 236756961, 236756964, 710270892, 710270895
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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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a(n) = a(n-1) + 3 if n odd.
a(n) = 3*a(n-1) if n even.
a(2n) = (11*3^n - 9)/2.
a(2n+1) = (11*3^n - 3)/2.
a(n) = 4*a(n-2) - 3*a(n-4) with n>3, a(0)=1, a(1)=4, a(2)=12, a(3)=15.
a(n) = Sum_{k=0..n} A220354(n,k) * 3^k.
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MAPLE
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seq( (11*3^floor(n/2) -3*(2+(-1)^n))/2, n=0..40); # G. C. Greubel, Nov 12 2019
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MATHEMATICA
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Table[(11*3^Floor[n/2] -3*(2+(-1)^n))/2, {n, 0, 40}] (* G. C. Greubel, Nov 12 2019 *)
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PROG
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(PARI) vector(41, n, (11*3^((n-1)\2) -3*(2-(-1)^n))/2) \\ G. C. Greubel, Nov 12 2019
(Magma) [(11*3^Floor(n/2) -3*(2+(-1)^n))/2: n in [0..40]]; // G. C. Greubel, Nov 12 2019
(Sage) [(11*3^floor(n/2) -3*(2+(-1)^n))/2 for n in (0..40)] # G. C. Greubel, Nov 12 2019
(GAP) List([0..40], n-> (11*3^Int(n/2) -3*(2+(-1)^n))/2 ); # G. C. Greubel, Nov 12 2019
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CROSSREFS
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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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