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A099392
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a(n) = floor((n^2 - 2*n + 3)/2).
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16
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1, 1, 3, 5, 9, 13, 19, 25, 33, 41, 51, 61, 73, 85, 99, 113, 129, 145, 163, 181, 201, 221, 243, 265, 289, 313, 339, 365, 393, 421, 451, 481, 513, 545, 579, 613, 649, 685, 723, 761, 801, 841, 883, 925, 969, 1013, 1059, 1105, 1153, 1201, 1251, 1301, 1353, 1405
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OFFSET
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1,3
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LINKS
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FORMULA
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G.f.: x *( -1+x-x^2-x^3 ) / ( (1+x)*(x-1)^3 ).
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
a(n+1) = (3 + 2*n^2 + (-1)^n)/4. (End)
a(n) = (2*n^2 - 4*n + 5 -(-1)^n)/4.
a(n+2) = a(n) + 2*n for n > 0.
a(n) = 2*A033683(n-1) - 1 for n > 0.
a(n) = A074148(n-1) - n + 2 for n > 1.
a(n) = 2*A290743(n-1) - 3 for n > 0.
Sum_{n>=1} 1/a(n) = tanh(Pi/2)*Pi/2 + coth(Pi/sqrt(2))*Pi/(2*sqrt(2)) + 1/2. - Amiram Eldar, Sep 16 2022
E.g.f.: ((2 - x + x^2)*cosh(x) + (3 - x + x^2)*sinh(x) - 2)/2. - Stefano Spezia, Jan 28 2024
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MATHEMATICA
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Array[Floor[(#^2 - 2 # + 3)/2] &, 54] (* or *)
Rest@ CoefficientList[Series[x (-1 + x - x^2 - x^3)/((1 + x) (x - 1)^3), {x, 0, 54}], x] (* Michael De Vlieger, Apr 21 2018 *)
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PROG
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CROSSREFS
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Differs from A085913 at n = 61. Apart from leading term, identical to A080827.
Partial sums: A212964(n) + n for n > 0.
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KEYWORD
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nonn,easy
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AUTHOR
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Ralf Stephan following a suggestion from Luke Pebody, Oct 20 2004
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STATUS
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approved
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