A128414
Riordan array ((1-2x)/(1+2x),x/(1+2x)^2).
Original entry on oeis.org
1, -4, 1, 8, -8, 1, -16, 36, -12, 1, 32, -128, 80, -16, 1, -64, 400, -400, 140, -20, 1, 128, -1152, 1680, -896, 216, -24, 1, -256, 3136, -6272, 4704, -1680, 308, -28, 1, 512, -8192, 21504, -21504, 10560, -2816
Offset: 0
Triangle begins
1;
-4, 1;
8, -8, 1;
-16, 36, -12, 1;
32, -128, 80, -16, 1;
-64, 400, -400, 140, -20, 1;
128, -1152, 1680, -896, 216, -24, 1;
-256, 3136, -6272, 4704, -1680, 308, -28, 1;
512, -8192, 21504, -21504, 10560, -2816, 416, -32, 1;
A247563
a(n) = 3*a(n-1) - 4*a(n-2) with a(0) = 2, a(1) = 3.
Original entry on oeis.org
2, 3, 1, -9, -31, -57, -47, 87, 449, 999, 1201, -393, -5983, -16377, -25199, -10089, 70529, 251943, 473713, 413367, -654751, -3617721, -8234159, -10231593, 2241857, 47651943, 133988401, 211357431, 98118689, -551073657, -2045695727, -3932792553, -3615594751
Offset: 0
G.f. = 2 + 3*x + x^2 - 9*x^3 - 31*x^4 - 57*x^5 - 47*x^6 + 87*x^7 + ...
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a247563 n = a247563_list !! n
a247563_list = 2 : 3 : zipWith (-) (map (* 3) $ tail a247563_list)
(map (* 4) a247563_list)
-- Reinhard Zumkeller, Sep 20 2014
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[n le 2 select n+1 else 3*Self(n-1)-4*Self(n-2): n in [1..40]]; // Vincenzo Librandi, Dec 05 2015
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m:=25; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((2 - 3*x)/(1-3*x+4*x^2))); // G. C. Greubel, Aug 04 2018
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{a[0], a[1]} = {2, 3}; a[n_] := a[n] = 3 a[n - 1] - 4 a[n - 2]; Table[a@ n, {n, 0, 32}] (* Michael De Vlieger, Dec 04 2015 *)
CoefficientList[Series[(2-3*x)/(1-3*x+4*x^2), {x, 0, 60}], x] (* G. C. Greubel, Aug 04 2018 *)
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{a(n) = if( n<0, n=-n; 4^-n, 1) * polcoeff( (2 - 3*x) / (1 - 3*x + 4*x^2) + x * O(x^n), n)};
A370846
a(n) = 5 + 4^n + 3*((-i*sqrt(7) - 3)^n + (i*sqrt(7) - 3)^n)/2^n.
Original entry on oeis.org
0, 24, 96, 168, 1200, 3960, 16128, 66888, 259152, 1052184, 4195488, 16759272, 67158000, 268359864, 1073772096, 4295178888, 17179113360, 68720897880, 274876666848, 1099509663528, 4398057364272, 17592161341944, 70368774872448, 281474983436232, 1125899763886800
Offset: 1
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Table[5 + 4^n + 3 ((-I Sqrt[7] - 3)^n + (I Sqrt[7] - 3)^n)/2^n, {n, 25}]
LinearRecurrence[{2, 7, 8, -16}, {0, 24, 96, 168}, 20]
CoefficientList[Series[-(24 x (-1 + 2 x) (1 + 4 x)/((-1 + x) (-1 + 4 x) (1 + 3 x + 4 x^2))), {x, 0, 20}], x]
Showing 1-3 of 3 results.
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