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A162958
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Equals A162956 convolved with (1, 3, 3, 3, ...).
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5
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1, 4, 10, 19, 25, 40, 67, 94, 100, 115, 142, 175, 208, 280, 388, 469, 475, 490, 517, 550, 583, 655, 763, 850, 883, 955, 1069, 1201, 1372, 1696, 2101, 2344, 2350, 2365, 2392, 2425, 2458, 2530, 2638, 2725, 2758, 2830, 2944, 3076, 3247, 3571, 3976, 4225, 4258
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OFFSET
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1,2
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COMMENTS
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Can be considered a toothpick sequence for N=3, following rules analogous to those in A160552 (= special case of "A"), A151548 = special case "B", and the toothpick sequence A139250 (N=2) = special case "C".
To obtain the infinite set of toothpick sequences, (N = 2, 3, 4, ...), replace the multiplier "2" in A160552 with any N, getting a triangle with 2^n terms. Convolve this A sequence with (1, N, 0, 0, 0, ...) = B such that row terms of A triangles converge to B.
Then generalized toothpick sequences (C) = A convolved with (1, N, N, N, ...).
A160552 * (1, 2, 2, 2, 2,...) = the toothpick sequence A139250 for N=2.
A162956 is analogous to A160552 but replaces "2" with the multiplier "3".
Row sums of "A"-type triangles = powers of (N+2); since row sums of A160552 = (1, 4, 16, 64, ...), while row sums of A162956 = (1, 5, 25, 125, ...).
Is there an illustration of this sequence using toothpicks? - Omar E. Pol, Dec 13 2016
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LINKS
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MAPLE
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b:= proc(n) option remember; `if`(n<2, n,
(j-> 3*b(j)+b(j+1))(n-2^ilog2(n)))
end:
a:= proc(n) option remember;
`if`(n=0, 0, a(n-1)+2*b(n-1)+b(n))
end:
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MATHEMATICA
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b[n_] := b[n] = If[n<2, n, Function[j, 3*b[j]+b[j+1]][n-2^Floor[Log[2, n]] ]];
a[n_] := a[n] = If[n == 0, 0, a[n-1] + 2*b[n-1] + b[n]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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