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A249013
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a(n) = floor( (n-1) * (n+4) / 10 ).
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3
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0, 0, 1, 2, 3, 5, 6, 8, 10, 12, 15, 17, 20, 23, 26, 30, 33, 37, 41, 45, 50, 54, 59, 64, 69, 75, 80, 86, 92, 98, 105, 111, 118, 125, 132, 140, 147, 155, 163, 171, 180, 188, 197, 206, 215, 225, 234, 244, 254, 264, 275, 285, 296, 307, 318, 330, 341, 353, 365
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OFFSET
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1,4
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COMMENTS
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LINKS
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FORMULA
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G.f.: x^3 * (1 + x^3 - x^4) / ((1 - x)^2 * (1 - x^5)) = x^3*(1+x^3-x^4)/ ( (1-x)^3*(1+x+x^2+x^3+x^4)).
a(n) = a(-3-n) for all n in Z.
a(n) = a(n-5) + n-1 for all n in Z.
a(n) + a(n+4) = min( a(n+1) + a(n+3), a(n+2) + a(n+2) ) + 1 for all n in Z.
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EXAMPLE
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G.f. = x^3 + 2*x^4 + 3*x^5 + 5*x^6 + 6*x^7 + 8*x^8 + 10*x^9 + 12*x^10 + ...
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MATHEMATICA
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a[ n_] := Quotient[ (n - 1) (n + 4), 10];
LinearRecurrence[{2, -1, 0, 0, 1, -2, 1}, {0, 0, 1, 2, 3, 5, 6}, 60] (* or *) CoefficientList[Series[x^2 (1 + x^3 - x^4) / ((1 - x)^2 (1 - x^5)), {x, 0, 60}], x] (* Vincenzo Librandi, Jan 10 2015 *)
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PROG
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(PARI) {a(n) = (n-1) * (n+4) \ 10};
(PARI) {a(n) = if( n<-1, n = -3-n); -(n<1) + polcoeff( x^3*(1 + x^3 - x^4) / ((1 - x)^2 * (1 - x^5)) + x * O(x^n), n)};
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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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