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A128918
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a(n) = n*(n+1)/2 if n is odd, otherwise (n-1)*n/2 + 1.
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6
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1, 1, 2, 6, 7, 15, 16, 28, 29, 45, 46, 66, 67, 91, 92, 120, 121, 153, 154, 190, 191, 231, 232, 276, 277, 325, 326, 378, 379, 435, 436, 496, 497, 561, 562, 630, 631, 703, 704, 780, 781, 861, 862, 946, 947, 1035, 1036, 1128, 1129, 1225, 1226, 1326, 1327, 1431, 1432, 1540
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5), with a(0)=1, a(1)=1, a(2)=2, a(3)=6, a(4)=7. - Harvey P. Dale, Mar 31 2012
a(n) = (1/2)*(-1)^n*(n+(-1)^n*((n-2)*n+2)-2). - Harvey P. Dale, Mar 31 2012
G.f.: (1 - x^2 + 4*x^3) / ((1 - x)^3*(1 + x)^2). - Colin Barker, Jan 20 2018
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MAPLE
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MATHEMATICA
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Table[If[OddQ[n], (n(n+1))/2, (n(n-1))/2+1], {n, 0, 60}] (* or *)
LinearRecurrence[{1, 2, -2, -1, 1}, {1, 1, 2, 6, 7}, 60] (* Harvey P. Dale, Mar 31 2012 *)
CoefficientList[ Series[(-4x^3 + x^2 -1)/((x -1)^3 (x + 1)^2), {x, 0, 55}], x] (* Robert G. Wilson v, Jan 20 2018 *)
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PROG
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(Haskell)
a128918 n = (n + m - 1) * n' + m * n - m + 1 where (n', m) = divMod n 2
(PARI) Vec((1 - x^2 + 4*x^3) / ((1 - x)^3*(1 + x)^2) + O(x^40)) \\ Colin Barker, Jan 20 2018
(Python)
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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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