

A179901


Triangle read by rows, antidiagonals of an array generated from (1, r, r, r,...) convolved with (1, 0, r, r, r,...).


2



1, 1, 1, 1, 2, 2, 1, 3, 4, 3, 1, 4, 6, 8, 4, 1, 5, 8, 15, 12, 5, 1, 6, 10, 24, 24, 16, 6, 1, 7, 12, 35, 40, 33, 20, 7, 1, 8, 14, 48, 60, 56, 42, 24, 8, 1, 9, 16, 63, 84, 85, 70, 51, 28, 9, 1, 10, 18, 80, 112, 120, 110, 88, 60, 32, 10, 1, 11, 20, 99, 144, 161, 156, 135, 104, 69, 36, 11
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,5


COMMENTS

Row sums = A179902: (1, 2, 5, 11, 23, 46, 87, 155,...)


LINKS

Table of n, a(n) for n=1..78.


FORMULA

Triangle read by rows, antidiagonals of an array generated from (1, r, r, r,...)
convolved with (1, 0, r, r, r,...); such than the rth row of the array =
(1, r, 2*r,...) then for n>3, a(n) = r^2 + a(n1).


EXAMPLE

First few rows of the array =
.
1,.1,..2,...3,...4,...5,...6,...7,....8,...
1,.2,..4,...8,..12,..16...20,..24,...28,... = A019442
1,.3,..6,..15,..24,..33,..42,..51,...60,... = A179805
1,.4,..8,..24,..40,..56,..70,..88,..104,...
.
Example: row 4 = (1, 4, 8, 24,...) = (1, 4, 4, 4,...) * (1, 0, 4, 4, 4,...)
= (1, r, 2*r, (2*r + r^2),...)
.
First few rows of the triangle =
.
1,
1, 1;
1, 2, 2;
1, 3, 4, 3;
1, 4, 6, 8, 4;
1, 5, 8, 15, 12, 5;
1, 6, 10, 24, 24, 16, 6;
1, 7, 12, 35, 40, 33, 20, 7;
1, 8, 14, 48, 60, 56, 42, 24, 8;
1, 9, 16, 63, 84, 85, 70, 51, 28, 9;
1, 10, 18, 80, 112, 120, 110, 88, 60, 32, 10;
1, 11, 20, 99, 144, 161, 156, 135, 104, 69, 36, 11;
1, 12, 22, 120, 180, 208, 210, 192, 160, 120, 78, 40, 12;
1, 13, 24, 143, 220, 261, 272, 259, 228, 185, 136, 87, 44, 13;
...


CROSSREFS

Cf. A019442, A179805
Sequence in context: A182630 A208805 A208514 * A209561 A283822 A210789
Adjacent sequences: A179898 A179899 A179900 * A179902 A179903 A179904


KEYWORD

nonn,tabf


AUTHOR

Gary W. Adamson, Jul 31 2010


STATUS

approved



