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A162148
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a(n) = n*(n+1)*(5*n+7)/6.
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6
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0, 4, 17, 44, 90, 160, 259, 392, 564, 780, 1045, 1364, 1742, 2184, 2695, 3280, 3944, 4692, 5529, 6460, 7490, 8624, 9867, 11224, 12700, 14300, 16029, 17892, 19894, 22040, 24335, 26784, 29392, 32164, 35105, 38220, 41514, 44992, 48659, 52520, 56580
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OFFSET
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0,2
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COMMENTS
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a(n) is the number of triples (w,x,y) havingt all terms in {0,...,n} and x+y>w. - Clark Kimberling, Jun 14 2012
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LINKS
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FORMULA
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G.f.: x*(4+x)/(1-x)^4.
a(n) = 4*binomial(n+2,3) + binomial(n+1,3).
a(n) = A091894(3,0)*binomial(n+2,3) + A091894(3,1)*binomial(n+1,3). (End)
a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4), a(0)=0, a(1)=4, a(2)=17, a(3)=44. - Harvey P. Dale, May 20 2014
E.g.f.: x*(24 +27*x +5*x^2)*exp(x)/6. - G. C. Greubel, Mar 31 2021
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MAPLE
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MATHEMATICA
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Table[(n(n+1)(5n+7))/6, {n, 0, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 4, 17, 44}, 50] (* Harvey P. Dale, May 20 2014 *)
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PROG
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(Sage) [n*(n+1)*(5*n+7)/6 for n in (0..50)] # G. C. Greubel, Mar 31 2021
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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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EXTENSIONS
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STATUS
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approved
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