A137531
a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3).
Original entry on oeis.org
1, 4, 10, 23, 53, 123, 286, 665, 1546, 3594, 8355, 19423, 45153, 104968, 244021, 567280, 1318766, 3065759, 7127025, 16568323, 38516678, 89540413, 208156206, 483904470, 1124941411, 2615171499, 6079536145, 14133206848, 32855719753, 76380281708, 177562612466
Offset: 0
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LinearRecurrence[{3, -2, 1}, {1, 4, 10}, 100] (* G. C. Greubel, Feb 17 2017 *)
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a=[1,4,10];for(i=1,99,a=concat(a,3*a[#a]-2*a[#a-1]+a[#a-2]));a \\ Charles R Greathouse IV, Jun 01 2011
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Vec((1 + x) / (1 - 3*x + 2*x^2 - x^3) + O(x^40)) \\ Colin Barker, Feb 17 2017
A159348
Transform of the finite sequence (1, 0, -1, 0, 1) by the T_{0,0} transform (see link).
Original entry on oeis.org
1, 1, 1, 4, 11, 24, 55, 128, 298, 693, 1611, 3745, 8706, 20239, 47050, 109378, 254273, 591113, 1374171, 3194560, 7426451, 17264404, 40134870, 93302253, 216901423, 504234633, 1172203306, 2725042075, 6334954246, 14726981894, 34236079265
Offset: 0
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I:=[11,24,55]; [1,1,1,4] 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 16 2018
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a(0):=1: a(1):=1:a(2):=1: a(3):=4:a(4):=11:a(5):=24:a(6):=55: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[{1,1,1,4},LinearRecurrence[{3,-2,1},{11,24,55},40]] (* or *) CoefficientList[Series[(-1+2 x-2 x^3+2 x^5-x^6)/(-1+3 x-2 x^2+x^3),{x,0,45}],x](* Harvey P. Dale, Oct 04 2011 *)
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m=50; v=concat([11, 24, 55], vector(m-3)); for(n=4, m, v[n]= 3*v[n-1] -2*v[n-2] +v[n-3]); concat([1,1,1,4], v) \\ G. C. Greubel, Jun 16 2018
A159349
Transform of the finite sequence (1, 0, -1, 0, 1, 0, -1) by the T_{0,0} transformation (see link).
Original entry on oeis.org
1, 1, 1, 4, 11, 24, 56, 129, 300, 698, 1623, 3773, 8771, 20390, 47401, 110194, 256170, 595523, 1384423, 3218393, 7481856, 17393205, 40434296, 93998334, 218519615, 507996473, 1180948523, 2745372238, 6382216141, 14836852470, 34491497366
Offset: 0
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I:=[56, 129, 300]; [1,1,1,4,11,24] 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 16 2018
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a(0):=1: a(1):=1:a(2):=1: a(3):=4:a(4):=11:a(5):=24:a(6):=56:a(7):=129:a(8):=300: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[{1, 1, 1, 4, 11, 24}, LinearRecurrence[{3, -2, 1}, {56, 129, 300}, 95]] (* G. C. Greubel, Jun 16 2018 *)
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m=50; v=concat([56,129,300], vector(m-3)); for(n=4, m, v[n]= 3*v[n-1] -2*v[n-2] +v[n-3]); concat([1,1,1,4,11,24], v) \\ G. C. Greubel, Jun 16 2018
A159350
Transform of A056594 by the T_{0,0} transformation (see link).
Original entry on oeis.org
1, 1, 1, 4, 11, 24, 54, 127, 297, 689, 1600, 3721, 8652, 20112, 46753, 108689, 252673, 587392, 1365519, 3174448, 7379698, 17155715, 39882197, 92714861, 215535904, 501060185, 1164823608, 2707886360, 6295072049, 14634267033, 34020543361
Offset: 0
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I:=[1,1,1,4,11]; [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 15 2018
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a(0):=1: a(1):=1: a(2):=1: a(3):=4: a(4):=11: 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}, {1,1,1,4,11}, 50] (* G. C. Greubel, Jun 15 2018 *)
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x='x+O('x^50); Vec((1-x)^2/((1-3*x+2*x^2-x^3)*(1+x^2))) \\ G. C. Greubel, Jun 15 2018
Showing 1-4 of 4 results.