Dintle N Kagiso has authored 3 sequences.
A282563
One third of the number of edges in the metrically regular triangulation of the n-th approximation of the Koch snowflake fractal.
Original entry on oeis.org
1, 8, 68, 596, 5300, 47444, 425972, 3829652, 34450484, 309988820, 2789637236, 25105686548, 225946984628, 2033506084436, 18301487651060, 164713120424084, 1482417010074932, 13341748795707092, 120075721981494644, 1080681429113975060
Offset: 1
a(1)=1, and there are three edges in a triangle. a(2)=8 and there are 24 edges in the second approximation of the Koch fractal.
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L:=[1,8]: for k from 3 to 30 do: L:=[op(L),13*L[k-1]-36*L[k-2]]: od: print(L);
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CoefficientList[Series[(1 - 5 x)/((1 - 4 x) (1 - 9 x)), {x, 0, 19}], x] (* or *) Table[(1/5) (4*9^# + 4^#) &[n + 1], {n, -1, 19}] (* Michael De Vlieger, Feb 18 2017 *)
LinearRecurrence[{13,-36},{1,8},30] (* Harvey P. Dale, Sep 22 2019 *)
A277492
Number of vertices in the metrically regular triangulation of the n-th approximation of the Koch snowflake fractal.
Original entry on oeis.org
3, 13, 96, 780, 6684, 58812, 523932, 4693884, 42158940, 379086396, 3410401308, 30688106748, 276170940636, 2485450385340, 22368701146524, 201316901032572, 1811846472148572, 16306595700758844, 146759271112516380, 1320833079235394556
Offset: 0
a(1) = 1+2+3+4+3 = 13 because an equilateral triangle can be cut up into 9 triangles with side length one-third which have 1+2+3+4 = 10 vertices and 3 further triangles yield 3 additional vertices.
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L:=[3,13,96]: for k from 4 to 34 do: L:=[op(L),13*L[k-1]-36*L[k-2]]: od: print(L);
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Table[(Boole[n == 0] 35/36) + (44*9^# + 21*4^#)/5 &[n - 1], {n, 0, 19}] (* or *)
CoefficientList[Series[(3 - 26 x + 35 x^2)/((1 - 4 x) (1 - 9 x)), {x, 0, 19}], x] (* Michael De Vlieger, Oct 21 2016 *)
LinearRecurrence[{13,-36},{3,13,96},30] (* Harvey P. Dale, Sep 17 2024 *)
A277491
Number of triangles in the standard triangulation of the n-th approximation of the Koch snowflake fractal.
Original entry on oeis.org
1, 12, 120, 1128, 10344, 93864, 847848, 7642920, 68835432, 619715496, 5578225896, 50207178792, 451877192040, 4066945060008, 36602706866664, 329425167106344, 2964829725182568, 26683480411545000, 240151375243512552, 2161362583350043176, 19452264074784109416
Offset: 0
a(1) = 9+3 = 12, because an equilateral triangle can be cut up into 9 triangles with side length one-third and 3 further triangles are stacked onto the three central side pieces.
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[(8*9^n-3*4^n)/5 : n in [0..30]]; // Wesley Ivan Hurt, Apr 11 2017
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L:=[1,12]: for k from 3 to 34 do: L:=[op(L),13*L[k-1]-36*L[k-2]]: od: print(L);
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Table[1/5*(8*9^n - 3*4^n), {n, 0, 20}] (* or *)
CoefficientList[Series[(1 - x)/((1 - 4 x) (1 - 9 x)), {x, 0, 20}], x] (* Michael De Vlieger, Nov 10 2016 *)
LinearRecurrence[{13,-36},{1,12},30] (* Harvey P. Dale, Feb 26 2023 *)
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Vec((1-x)/((1-4*x)*(1-9*x)) + O(x^30)) \\ Colin Barker, Oct 19 2016
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