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A092353
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Expansion of (1+x^3)/((1-x)^2*(1-x^3)^2).
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4
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1, 2, 3, 7, 11, 15, 24, 33, 42, 58, 74, 90, 115, 140, 165, 201, 237, 273, 322, 371, 420, 484, 548, 612, 693, 774, 855, 955, 1055, 1155, 1276, 1397, 1518, 1662, 1806, 1950, 2119, 2288, 2457, 2653, 2849, 3045, 3270, 3495, 3720, 3976, 4232, 4488, 4777, 5066, 5355, 5679
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (1+x^3)/((1-x)^2*(1-x^3)^2) = (1+x^3)/((1-x)^4*(1+x+x^2)^2).
a(n) = (1/2)*(-4*t^3 + (2n-7)*t^2 + (4n-1)*t +2n +2), where t = floor(n/3). - Ridouane Oudra, Oct 19 2019
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MAPLE
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seq(add(floor(i/3)^2, i=1..n+3), n=0..60); # Ridouane Oudra, Oct 19 2019
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MATHEMATICA
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a[n_] := Sum[Floor[i/3]^2, {i, 1, n+3}]; Table[a[n], {n, 0, 100}] (* Enrique Pérez Herrero, Mar 20 2012 *)
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PROG
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(Sage)
a, b, c, m = 0, 0, 0, 0
while True:
yield (a*(a*(2*a+9)+13)+b*(b+1)*(2*b+1)+c*(c+1)*(2*c+1)+6)//6
m = m + 1 if m < 2 else 0
if m == 0: a += 1
elif m == 1: b += 1
elif m == 2: c += 1
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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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