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A171662
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a(n) = floor((2*n^2 + n)/6).
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2
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0, 0, 1, 3, 6, 9, 13, 17, 22, 28, 35, 42, 50, 58, 67, 77, 88, 99, 111, 123, 136, 150, 165, 180, 196, 212, 229, 247, 266, 285, 305, 325, 346, 368, 391, 414, 438, 462, 487, 513, 540, 567, 595, 623, 652, 682, 713, 744, 776, 808, 841, 875, 910, 945
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) = floor(n*(2*n + 1)/6).
a(n) = A078617(-1 - n) for all n in Z.
G.f.: -x^2*(x^4 + x^2 + x + 1)/( (x+1) * (x^2+x+1) * (x^2-x+1) * (x-1)^3). - Alois P. Heinz, Jun 24 2013
a(n) = 2*a(n-1) - a(n-2) + a(n-6) - 2*a(n-7) + a(n-8); a(0)=0, a(1)=0, a(2)=1, a(3)=3, a(4)=6, a(5)=9, a(6)=13, a(7)=17. - Harvey P. Dale, Oct 15 2014
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MATHEMATICA
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Table[Floor[(2n^2+n)/6], {n, 0, 60}] (* or *) LinearRecurrence[{2, -1, 0, 0, 0, 1, -2, 1}, {0, 0, 1, 3, 6, 9, 13, 17}, 60] (* Harvey P. Dale, Oct 15 2014 *)
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PROG
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(PARI) {a(n) = (2 * n^2 + n) \ 6};
(Magma) [Floor((2*n^2+n)/6): n in [0..60]]; // G. C. Greubel, Sep 25 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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