

A174068


Convolved with its aerated variant of two zeros between terms = A000041


3



1, 1, 2, 2, 4, 5, 7, 9, 13, 17, 23, 29, 38, 48, 62, 77, 98, 121, 153, 187, 233, 283, 349, 422, 515, 620, 751, 900, 1083, 1291, 1544, 1832, 2180, 2576, 3050, 3590, 4234, 4965, 5830, 6813, 7971, 9286, 10824, 12572, 14608, 16921, 19600, 22640, 26150, 30130, 34709
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OFFSET

0,3


COMMENTS

Considered k=3 in an infinite set of convolution sequences: (aerated with
one zero, A174065; two zeros, A174068); such that A000041 =
(1, 1, 2, 3, 5, 7, 11,...) = (1, 1, 2, 2, 4, 5, 7, 9, 13, 17,...) *
(1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 4, 0, 0, 5, 0, 0, 7, 0, 0,...).


LINKS

Table of n, a(n) for n=0..50.


FORMULA

Refer to A174065, and A174066, the case for k=3. The sequence = left border
of a triangle generated from 3 rules: row sums = A000041; columns >1 are
shifted down thrice from previous column; column terms are derived from
selfconvolution of left border, (with the left border placed at top as a
heading).
A(x)*A(x^3) = A000041(x) for the generating functions. [From R. J. Mathar, Mar 18 2010]
Expansion of f(x^3)/f(x) * f(x^27)/f(x^9) * f(x^243)/f(x^27) * ... where f(x) is a Ramanujan theta function.  Michael Somos, Jun 07 2012


EXAMPLE

The triangle heading and first few rows of the triangle =
1, 1, 2, 2, 4, 5, 7,...
1;
1;
2;
2, 1;
4, 1;
5, 2;
7, 2, 2;
...
G.f. = 1 + x + 2*x^2 + 2*x^3 + 4*x^4 + 5*x^5 + 7*x^6 + 9*x^7 + 13*x^8 + 17*x^9 + ...


CROSSREFS

A000041, A174065, A174066, A174067
Sequence in context: A128663 A206557 A240508 * A135833 A137200 A026930
Adjacent sequences: A174065 A174066 A174067 * A174069 A174070 A174071


KEYWORD

nonn


AUTHOR

Gary W. Adamson, Mar 06 2010


EXTENSIONS

More terms from R. J. Mathar, Mar 18 2010


STATUS

approved



