A159341
Transform of the finite sequence (1, 0, -1, 0, 1) by the T_{0,1} transformation (see link).
Original entry on oeis.org
2, 3, 6, 16, 39, 89, 206, 479, 1114, 2590, 6021, 13997, 32539, 75644, 175851, 408804, 950354, 2209305, 5136011, 11939777, 27756614, 64526299, 150005446, 348720354, 810676469, 1884594145, 4381149851, 10184937732, 23677107639, 55042597304
Offset: 0
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I:=[39, 89, 206]; [2, 3, 6, 16] cat [n le 3 select I[n] else 3*Self(n-1) - 2*Self(n-2) + Self(n-3): n in [1..30]]; // G. C. Greubel, Jun 25 2018
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a(0):=2: a(1):=3:a(2):=6: a(3):=16:a(4):=39:a(5):=89:a(6):=206:for n from 4 to 31 do a(n+3):=3*a(n+2)-2*a(n+1)+a(n):od:seq(a(i),i=0..31);
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Join[{2, 3, 6, 16}, LinearRecurrence[{3, -2, 1}, {39, 89, 206}, 47]] (* G. C. Greubel, Jun 25 2018 *)
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z='z+O('z^30); Vec(((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2+z^4) + ((1-z+z^2)/(1-3*z+2*z^2-z^3))) \\ G. C. Greubel, Jun 25 2018
A159342
Transform of the finite sequence (1, 0, -1, 0, 1, 0, -1) by the T_{0,1} transform (see link).
Original entry on oeis.org
2, 3, 6, 16, 39, 89, 207, 480, 1116, 2595, 6033, 14025, 32604, 75795, 176202, 409620, 952251, 2213715, 5146263, 11963610, 27812019, 64655100, 150304872, 349416435, 812294661, 1888355985, 4389895068, 10205267895, 23724369534, 55152467880
Offset: 0
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I:=[207, 480, 1116]; [2, 3, 6, 16, 39, 89] cat [n le 3 select I[n] else 3*Self(n-1) - 2*Self(n-2) +Self(n-3): n in [1..50]]; // G. C. Greubel, Jun 17 2018
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a(0):=2: a(1):=3:a(2):=6: a(3):=16:a(4):=39:a(5):=89:a(6):=207:a(7):=480:a(8):=1116:for n from 6 to 31 do a(n+3):=3*a(n+2)-2*a(n+1)+a(n):od:seq(a(i),i=0..31);
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Join[{2, 3, 6, 16, 39, 89}, LinearRecurrence[{3, -2, 1}, {207, 480, 1116}, 50]] (* G. C. Greubel, Jun 17 2018 *)
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m=50; v=concat([207, 480, 1116], vector(m-3)); for(n=4, m, v[n] = 3*v[n-1] -2*v[n-2] +v[n-3]); concat([2, 3, 6, 16, 39, 89], v) \\ G. C. Greubel, Jun 17 2018
A159343
Transform of A056594 by the T_{0,1} transformation (see link).
Original entry on oeis.org
2, 3, 6, 16, 39, 89, 205, 478, 1113, 2586, 6010, 13973, 32485, 75517, 175554, 408115, 948754, 2205584, 5127359, 11919665, 27709861, 64417610, 149752773, 348132962, 809310950, 1881419697, 4373770153, 10167782017, 23637225442, 54949882443
Offset: 0
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I:=[2, 3, 6, 16, 39]; [n le 5 select I[n] else 3*Self(n-1) -3*Self(n-2) +4*Self(n-3) -2*Self(n-4) +Self(n-5): n in [1..50]]; // G. C. Greubel, Jun 17 2018
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a(0):=2: a(1):=3:a(2):=6: a(3):=16:a(4):=39:for n from 0 to 31 do a(n+5):=3*a(n+4)-3*a(n+3)+4*a(n+2)-2*a(n+1)+a(n):od:seq(a(i),i=0..31);
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LinearRecurrence[{3, -3, 4, -2, 1}, {2, 3, 6, 16, 39}, 50] (* G. C. Greubel, Jun 17 2018 *)
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m=32; v=concat([2, 3, 6, 16, 39], vector(m-5)); for(n=6, m, v[n] = 3*v[n-1] -3*v[n-2] +4*v[n-3] -2*v[n-4] +v[n-5]); v \\ G. C. Greubel, Jun 17 2018
Showing 1-3 of 3 results.