

A162958


Equals A162956 convolved with (1, 3, 3, 3, ...).


5



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

1,2


COMMENTS

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, ...).
Examples: A160552 * (1, 2, 0, 0, 0,...) = a Btype sequence A151548.
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 terms of A162956 tend to A162957 = (1, 3, 0, 0, 0, ...) * A162956.
Toothpick sequence for N = 3 = A162958 = A162956 * (1, 3, 3, 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


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..16384
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n1)1) for n >= 2.]
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS


MAPLE

b:= proc(n) option remember; `if`(n<2, n,
(j> 3*b(j)+b(j+1))(n2^ilog2(n)))
end:
a:= proc(n) option remember;
`if`(n=0, 0, a(n1)+2*b(n1)+b(n))
end:
seq(a(n), n=1..100); # Alois P. Heinz, Jan 28 2017


MATHEMATICA

b[n_] := b[n] = If[n<2, n, Function[j, 3*b[j]+b[j+1]][n2^Floor[Log[2, n]] ]];
a[n_] := a[n] = If[n == 0, 0, a[n1] + 2*b[n1] + b[n]];
Array[a, 100] (* JeanFrançois Alcover, Jun 11 2018, after Alois P. Heinz *)


CROSSREFS

Cf. A139250, A152548, A160552, A162956, A163267.
Third diagonal of A163311.
Sequence in context: A318070 A073262 A145731 * A029714 A062198 A050858
Adjacent sequences: A162955 A162956 A162957 * A162959 A162960 A162961


KEYWORD

nonn


AUTHOR

Gary W. Adamson, Jul 18 2009


EXTENSIONS

Clarified definition by Omar E. Pol, Feb 06 2017


STATUS

approved



