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<a href="/index/Rec#order_0209">Index entries for linear recurrences with constant coefficients</a>, signature (20, -146, 480, -657, 60, 660, -400, -144, 128).

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With[{r = 4 + 2 # - 5 #^2 + #^3 &}, Table[8^n + n/2 - n RootSum[r, -494 #^n + 12 #1^(n + 1) + 35 #^(n + 2) &]/458 - RootSum[r, #^n &] - 1, {n, 20}]] // RootReduce

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1, 30, 323, 3110, 27777, 237498, 1977439, 16202990, 131490509, 1060894002, 8529819531, 68439823942, 548461371993, 4392080943978, 35156984457463, 281349668446430, 2251228221924645, 18011798305060578, 144103388698943651, 1152868080218482102, 9223130638279472433

3,1

1,2

Sequence extended to n=1 using formula/recurrence.

<a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20, -146, 480, -657, 60, 660, -400, -144, 128).

a(n) = 20*a(n-1)-146*a(n-2)+480*a(n-3)-657*a(n-4)+60*a(n-5)+660*a(n-6)-400*a(n-7)-144*a(n-8)+128*a(n-9).

G.f.: x*(-1 - 10*x + 131*x^2 - 550*x^3 + 1008*x^4 - 628*x^5 + 128*x^6 - 448*x^7 + 384*x^8)/((-1 + 8*x)*(-1 + 6*x - 7*x^2 - 2*x^3 + 4*x^4)^2).

LinearRecurrence[{20, -146, 480, -657, 60, 660, -400, -144, 128}, {1, 30, 323, 3110, 27777, 237498, 1977439, 16202990, 131490509}, 20]

CoefficientList[Series[(-1 - 10 x + 131 x^2 - 550 x^3 + 1008 x^4 - 628 x^5 + 128 x^6 - 448 x^7 + 384 x^8)/((-1 + 8 x) (-1 + 6 x - 7 x^2 - 2 x^3 + 4 x^4)^2), {x, 0, 20}], x]

With[{r = 4 + 2 # - 5 #^2 + #^3 &}, Table[8^n + n/2 - n RootSum[r, -494 #^n + 12 #1^(n + 1) + 35 #^(n + 2) &]/458 - RootSum[r, #^n &] - 1, {n, 20}]] // RootReduce

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323, 3110, 27777, 237498, 1977439, 16202990, 131490509, 1060894002, 8529819531, 68439823942, 548461371993, 4392080943978, 35156984457463, 281349668446430, 2251228221924645, 18011798305060578, 144103388698943651, 1152868080218482102, 9223130638279472433

a(n) = 2^(3*n) - 1 - A286187(n). - Pontus von Brömssen, Apr 23 2023

Cf. A286187.

nonn,more,new

More terms (based on data in A286187) from Pontus von Brömssen, Apr 23 2023

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