Original entry on oeis.org
0, 2, 12, 58, 256, 1072, 4336, 17112, 66304, 253280, 956608, 3579680, 13292544, 49039360, 179912448, 656874368, 2388205568, 8650598912, 31231020032, 112419973632, 403596148736, 1445463642112, 5165581660160, 18423238924288
Offset: 0
-
a:=[0,2,12,58];; for n in [5..30] do a[n]:=8*a[n-1]-20*a[n-2] +16*a[n-3]-4*a[n-4]; od; a; # G. C. Greubel, Jul 31 2019
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R:=PowerSeriesRing(Integers(), 30); [0] cat Coefficients(R!( 2*x*(1-x)^2/(1-4*x+2*x^2)^2 )); // G. C. Greubel, Jul 31 2019
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LinearRecurrence[{8,-20,16,-4}, {0,2,12,58}, 30] (* G. C. Greubel, Jul 31 2019 *)
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my(x='x+O('x^30)); concat([0], Vec(2*x*(1-x)^2/(1-4*x+2*x^2)^2)) \\ G. C. Greubel, Jul 31 2019
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(2*x*(1-x)^2/(1-4*x+2*x^2)^2).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jul 31 2019
A054147
a(n) = T(2n,n), array T as in A054144.
Original entry on oeis.org
0, 3, 21, 108, 492, 2100, 8604, 34272, 133728, 513648, 1948560, 7318080, 27256896, 100815936, 370684608, 1355996160, 4938304512, 17914202880, 64760732928, 233390693376, 838784916480, 3006980379648, 10755352869888
Offset: 0
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a:=[0,3,21,108];; for n in [5..30] do a[n]:=8*a[n-1]-20*a[n-2] +16*a[n-3]-4*a[n-4]; od; a; # G. C. Greubel, Jul 31 2019
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R:=PowerSeriesRing(Integers(), 30); [0] cat Coefficients(R!( 3*x*(1-x)/(1-4*x+2*x^2)^2 )); // G. C. Greubel, Jul 31 2019
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LinearRecurrence[{8,-20,16,-4}, {0,3,21,108}, 30] (* G. C. Greubel, Jul 31 2019 *)
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my(x='x+O('x^30)); concat([0], Vec(3*x*(1-x)/(1-4*x+2*x^2)^2)) \\ G. C. Greubel, Jul 31 2019
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(3*x*(1-x)/(1-4*x+2*x^2)^2).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jul 31 2019
Original entry on oeis.org
1, 5, 28, 132, 574, 2380, 9560, 37536, 144872, 551696, 2078464, 7761600, 28771168, 105985984, 388336256, 1416262656, 5144067200, 18616720640, 67159278592, 241579840512, 866744413696, 3102440074240, 11081272653824
Offset: 0
Original entry on oeis.org
1, 14, 84, 410, 1820, 7648, 31008, 122584, 475600, 1818656, 6874560, 25742624, 95645888, 353032960, 1295729664, 4732541824, 17211685120, 62362187264, 225201546240, 810825419264, 2911520685056, 10429433085952
Offset: 1
Original entry on oeis.org
0, 1, 6, 29, 128, 536, 2168, 8556, 33152, 126640, 478304, 1789840, 6646272, 24519680, 89956224, 328437184, 1194102784, 4325299456, 15615510016, 56209986816, 201798074368, 722731821056, 2582790830080, 9211619462144
Offset: 0
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a:=[0,1,6,29];; for n in [5..30] do a[n]:=8*a[n-1]-20*a[n-2] +16*a[n-3]-4*a[n-4]; od; a; # G. C. Greubel, Aug 01 2019
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R:=PowerSeriesRing(Integers(), 30); [0] cat Coefficients(R!( x*(1-x)^2/(1-4*x+2*x^2)^2 )); // G. C. Greubel, Aug 01 2019
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LinearRecurrence[{8,-20,16,-4}, {0,1,6,29}, 30] (* G. C. Greubel, Aug 01 2019 *)
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my(x='x+O('x^30)); concat([0], Vec(x*(1-x)^2/(1-4*x+2*x^2)^2)) \\ G. C. Greubel, Aug 01 2019
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(x*(1-x)^2/(1-4*x+2*x^2)^2).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Aug 01 2019
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