A171068
G.f. -x*(x-1)*(1+x)/(1-x-11*x^2-x^3+x^4).
Original entry on oeis.org
0, 1, 1, 11, 23, 144, 407, 2003, 6601, 28897, 103104, 425569, 1582009, 6337475, 24062039, 94930704, 364368599, 1426330907, 5505254161, 21464332033, 83084090112, 323270665729, 1253154734833, 4870751815931, 18895640474711
Offset: 0
R. J. Mathar, at the request of R. K. Guy, Sep 03 2010
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I:=[0, 1, 1, 11]; [n le 4 select I[n] else Self(n-1) + 11*Self(n-2) + Self(n-3) - Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 19 2012
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CoefficientList[Series[-x*(x - 1)*(1 + x)/(1 - x - 11*x^2 - x^3 + x^4), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 19 2012 *)
A171069
G.f. -x*(x-1)*(1+x)/(1-x-12*x^2-x^3+x^4).
Original entry on oeis.org
0, 1, 1, 12, 25, 169, 480, 2521, 8425, 38988, 142129, 615889, 2352000, 9845809, 38543569, 158429388, 628446025, 2558296441, 10219534560, 41389108489, 165953373625, 670283913612, 2692893971041, 10860865199521, 43679923392000
Offset: 0
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I:=[0, 1, 1, 12]; [n le 4 select I[n] else Self(n-1) + 12*Self(n-2) + Self(n-3) - Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 19 2012
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CoefficientList[Series[-x*(x - 1)*(1 + x)/(1 - x - 12*x^2 - x^3 + x^4), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 19 2012 *)
LinearRecurrence[{1,12,1,-1},{0,1,1,12},30] (* Harvey P. Dale, Nov 04 2024 *)
A218136
Norm of coefficients in the expansion of 1 / (1 - 3*x + 2*I*x^2), where I^2=-1.
Original entry on oeis.org
1, 9, 85, 873, 8845, 89505, 906373, 9177849, 92932285, 941010705, 9528455221, 96482899305, 976963204333, 9892500250113, 100169136977125, 1014289183762137, 10270454347410973, 103996211523970545, 1053041242918825621, 10662848608027795785, 107969503760905131085
Offset: 0
G.f.: A(x) = 1 + 9*x + 85*x^2 + 873*x^3 + 8845*x^4 + 89505*x^5 + 906373*x^6 +...
The terms equal the norm of the complex coefficients in the expansion:
1/(1-3*x+2*I*x^2) = 1 + 3*x + (9 - 2*I)*x^2 + (27 - 12*I)*x^3 + (77 - 54*I)*x^4 + (207 - 216*I)*x^5 + (513 - 802*I)*x^6 + (1107 - 2820*I)*x^7 +...
so that
a(1) = 3^2, a(2) = 9^2 + 2^2, a(3) = 27^2 + 12^2, a(4) = 77^2 + 54^2, a(5) = 207^2 + 216^2, ...
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CoefficientList[Series[(1-4x^2)/(1-9x-8x^2-36x^3+16x^4),{x,0,20}],x] (* or *) LinearRecurrence[{9,8,36,-16},{1,9,85,873},30] (* Harvey P. Dale, Mar 22 2023 *)
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{a(n)=norm(polcoeff(1/(1-3*x+2*I*x^2+x*O(x^n)), n))}
for(n=0,30,print1(a(n),", "))
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