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A243230
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Number of isoscent sequences of length n with exactly four ascents.
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2
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2, 172, 3048, 33065, 275641, 1945529, 12246616, 70948683, 386155045, 2002805428, 10000176270, 48434098918, 228855387073, 1059660102823, 4824874714701, 21663637862920, 96134931734425, 422409581103433, 1840542075175555, 7962723214375505, 34240149114971395
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OFFSET
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7,1
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LINKS
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FORMULA
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G.f.: x^7*(2 + 58*x - 3648*x^2 + 72673*x^3 - 842380*x^4 + 6646402*x^5 - 38326607*x^6 + 167767231*x^7 - 568689800*x^8 + 1503499267*x^9 - 3082877524*x^10 + 4785455208*x^11 - 5266898088*x^12 + 3276181912*x^13 + 633509453*x^14 - 3771906622*x^15 + 3792580950*x^16 - 1396200816*x^17 - 686750857*x^18 + 1195721330*x^19 - 1109678200*x^20 + 1163509247*x^21 - 851661184*x^22 + 47666957*x^23 + 460007148*x^24 - 312042368*x^25 - 2183667*x^26 + 84057866*x^27 - 24458487*x^28 - 9560501*x^29 + 5700026*x^30 + 307683*x^31 - 694453*x^32 + 45182*x^33 + 51672*x^34 - 3534*x^35 - 1395*x^36 - 135*x^37) / ((1 - x)^5*(1 - 2*x)^4*(1 - 4*x + 3*x^2 + x^3)^3*(1 - 8*x + 21*x^2 - 18*x^3 - 3*x^4 + 5*x^5 + 3*x^6)^2*(1 - 16*x + 105*x^2 - 361*x^3 + 676*x^4 - 606*x^5 + 68*x^6 + 192*x^7 + 83*x^8 - 157*x^9 - 44*x^10 + 45*x^11 + 15*x^12)) (conjectured). - Colin Barker, May 05 2019
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MAPLE
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b:= proc(n, i, t) option remember; `if`(n<1, 1, expand(add(
`if`(j>i, x, 1) *b(n-1, j, t+`if`(j=i, 1, 0)), j=0..t+1)))
end:
a:= n-> coeff(b(n-1, 0$2), x, 4):
seq(a(n), n=7..35);
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MATHEMATICA
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b[n_, i_, t_] := b[n, i, t] = If[n < 1, 1, Expand[Sum[
If[j > i, x, 1] *b[n - 1, j, t + If[j == i, 1, 0]], {j, 0, t + 1}]]];
a[n_] := Coefficient[b[n - 1, 0, 0], x, 4];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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