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A054460
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A001333(n), n >= 1, convolved twice with itself.
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2
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1, 9, 48, 204, 765, 2649, 8680, 27312, 83313, 247985, 723624, 2077164, 5880797, 16454865, 45577200, 125130432, 340882113, 922265721, 2479938368, 6631802220, 17646603933, 46744464745, 123314065944, 324085913136, 848801213425
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OFFSET
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0,2
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COMMENTS
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a(n) = A054458(n+2,2) (third column of convolution triangle).
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LINKS
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FORMULA
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a(n) = (n+1)*(LP2(n+1)+2*LP2(n)+LP2(n-1))/8, n >= 1, LP2(n) = A054459(n), a(0) = 1.
a(n) = (n+1)*((10*n+11)*LP(n)+(4*n+5)*LP(n-1))/16, n >= 1, LP(n) = A001333(n+1).
G.f.: ((1+x)/(1-2*x-x^2))^3.
a(n) = +6*a(n-1) -9*a(n-2) -4*a(n-3) +9*a(n-4) +6*a(n-5) +a(n-6). - R. J. Mathar, Feb 05 2024
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MATHEMATICA
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LinearRecurrence[{6, -9, -4, 9, 6, 1}, {1, 9, 48, 204, 765, 2649}, 30] (* Paolo Xausa, Feb 06 2024 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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