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A178947
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Expansion of x*(1+2*x+8*x^2+3*x^4+4*x^3) / ( (1+x)^2*(x-1)^4 ).
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1
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1, 4, 17, 38, 81, 138, 229, 340, 497, 680, 921, 1194, 1537, 1918, 2381, 2888, 3489, 4140, 4897, 5710, 6641, 7634, 8757, 9948, 11281, 12688, 14249, 15890, 17697, 19590, 21661, 23824, 26177, 28628, 31281, 34038, 37009, 40090, 43397, 46820, 50481, 54264, 58297
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OFFSET
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1,2
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COMMENTS
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Let S(x) be the generating function of A016777; then the generating function of this sequence is x/2 * ((S(x)^2 + S(x^2)): the sequence is obtained by adding half of the convolution square, A100175, and the aerated A016777.
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LINKS
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FORMULA
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a(n) = (-1+(-1)^n+(7-3*(-1)^n)*n-6*n^2+6*n^3)/8.
a(n) = (3*n^3-3*n^2+2*n)/4 for n even.
a(n) = (3*n^3-3*n^2+5*n-1)/4 for n odd.
a(n) = 2*a(n-1)+a(n-2)-4*a(n-3)+a(n-4)+2*a(n-5)-a(n-6) for n>6.
(End)
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EXAMPLE
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(1/2) * ((1, 8, 30, 76, 155, 276,...) + (1, 0, 4, 0, 7, 0, 10,...)) = (1, 4, 17, 38, 81, 138, 229,...).
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MATHEMATICA
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LinearRecurrence[{2, 1, -4, 1, 2, -1}, {1, 4, 17, 38, 81, 138}, 50] (* Harvey P. Dale, Jun 12 2018 *)
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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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