

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
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



