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A271638
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The total sum of the cubes of all parts of all compositions of n.
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1
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1, 10, 48, 170, 512, 1398, 3580, 8770, 20808, 48206, 109652, 245850, 544864, 1196134, 2605164, 5636210, 12124280, 25952382, 55312516, 117440650, 248512656, 524288150, 1103102108, 2315255970, 4848615592, 10133438638, 21139292340, 44023414970, 91536490688
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: x*(1 + 4*x + x^2)/((1 - 2*x)*(1 - x))^2.
a(n) = (13*n - 36)*2^(n - 1) + 6*n + 18.
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EXAMPLE
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The two compositions of n=2 are 2 and 1+1. The total sum of the cubes is a(2) = 2^3+1^3+1^3 = 10.
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MATHEMATICA
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Table[(13 n - 36) 2^(n - 1) + 6 n + 18, {n, 29}] (* or *)
Rest@ CoefficientList[Series[x (1 + 4 x + x^2)/((1 - 2 x) (1 - x))^2, {x, 0, 29}], x] (* Michael De Vlieger, Apr 11 2016 *)
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PROG
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(PARI) x='x+O('x^99); Vec(x*(1+4*x+x^2)/((2*x-1)*(1-x))^2) \\ Altug Alkan, Apr 11 2016
(Python) for n in range(1, 50):print((13*n-36)*2**(n-1)+6*n+18) # Soumil Mandal, Apr 11 2016
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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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