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A229620
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Incorrect version of A045949.
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0
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0, 6, 38, 116, 256, 478, 798, 1236, 1808, 2534, 3430, 4516, 5808, 7326, 9086, 11108, 13408, 16006, 18918, 22164, 25760, 29726, 34078, 38836, 44016, 49638, 55718, 62276, 69328, 76894, 84990, 93636, 102848, 112646, 123046, 134068, 145728, 158046, 171038, 184724, 199120, 214246, 230118, 246756, 264176, 282398, 301438, 321316, 342048, 363654
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OFFSET
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0,2
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COMMENTS
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Arises from the formula in Problem 11 of Zhuravlev and Samovol (2012) paper, which incorrectly claims it to produce sequence A045949. Terms a(n) for n<=3 match those of A045949 but afterwards the two sequences diverge. Nevertheless these sequences satisfy the same linear recurrent relation.
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LINKS
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FORMULA
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For even n, a(n) = n*(6*n^2+9*n-4)/2; for odd n, a(n) = (n+1)*(6*n^2+3*n+1)/2 - 4*n.
For n>=4, a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-2) + 3*a(n-3) - a(n-4).
a(n) = (1-(-1)^n-8*n+18*n^2+12*n^3)/4. G.f.: -2*x*(2*x+1)*(x^2-4*x-3) / ((x-1)^4*(x+1)). - Colin Barker, Sep 29 2013
E.g.f.: (x*(11 + 27*x + 6*x^2)*cosh(x) + (1 + 11*x + 27*x^2 + 6*x^3)*sinh(x))/2. - Stefano Spezia, Mar 20 2022
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PROG
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(PARI) { a(n) = if(n%2, (n+1)*(6*n^2+3*n+1)/2- 4*n, n*(6*n^2+9*n-4)/2 ) }
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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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