editing

approved

Analogue Analog of A094091 for S=4.

approved

editing

_Joshua Zucker (joshua.zucker(AT)gmail.com), _, Jul 23 2006

Duplicate Analogue of A105306A094091 for S=4.

1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0, 0, 0, 1, 4, 5, 3, 1, 8, 12, 9, 4, 0, 0, 0, 0, 1, 16, 28, 25, 14, 5, 1, 32, 64, 66, 44, 20, 6, 0, 0, 1, 640, 0, 0, 0

0,4

1,1

A finite sequence of length 28.

The old entry with this A-number was a duplicate of A105306.

Cf. A094091, A106197.

dead

nonn,fini,full

Joshua Zucker (joshua.zucker(AT)gmail.com), Jul 23 2006

Triangle, row sums = odd indexed Fibonacci numbers.

Duplicate of A105306.

1, 1, 1, 2, 2, 1, 4, 5, 3, 1, 8, 12, 9, 4, 1, 16, 28, 25, 14, 5, 1, 32, 64, 66, 44, 20, 6, 1, 64, 144, 168, 129, 70, 27, 7, 1

A is the array:

1, 0, 0, 0, 0, 0,...

0, 1, 0, 0, 0, 0,...

1, 0, 1, 0, 0, 0,...

0, 2, 0, 1, 0, 0,...

1, 0, 3, 0, 1, 0,...

0, 3, 0, 4, 0, 1,...

...

i.e. columns are bin(n,k) with alternating zeros.

Row sums = 1, 2, 5, 13, 34, 89, 233...

V.E. Hoggatt, Jr., and Marjorie Bicknell, editors: "A Primer for the Fibonacci Numbers", 1970, p. 87

Let P = the infinite lower triangular Pascal's Triangle matrix (A007318) and A = an array composed of bin(n, k; k=0, 1, 2)columns with alternating zeros.) Perform P * A and extract antidiagonals which become the rows of A106197.

Forming P * A, we get the following triangle (as a matrix, fill in the spaces with zeros):

1;

1, 1;

2, 2, 1;

4, 5, 3, 1;

8, 12, 9, 4, 1;

16, 28 25, 14, 5, 1;

32, 64, 66, 44, 20, 6, 1;

64, 144, 168, 129, 70, 27, 7, 1;

...

Cf. A045613, A006809, A062109.

nonn,tabl,new

dead

Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 24 2005

Let P = the infinite lower triangular Pascal's Triangle matrix (A007318), and A = an array composed of bin(n, k; k=0, 1, 2)columns with alternating zeros.) Perform P * A and extract antidiagonals which become the rows of A106197.

nonn,tabl,new

Triangle, row sums = odd indexed Fibonacci numbers.

1, 1, 1, 2, 2, 1, 4, 5, 3, 1, 8, 12, 9, 4, 1, 16, 28, 25, 14, 5, 1, 32, 64, 66, 44, 20, 6, 1, 64, 144, 168, 129, 70, 27, 7, 1

0,4

A is the array:

1, 0, 0, 0, 0, 0,...

0, 1, 0, 0, 0, 0,...

1, 0, 1, 0, 0, 0,...

0, 2, 0, 1, 0, 0,...

1, 0, 3, 0, 1, 0,...

0, 3, 0, 4, 0, 1,...

...

i.e. columns are bin(n,k) with alternating zeros.

Row sums = 1, 2, 5, 13, 34, 89, 233...

V.E. Hoggatt, Jr., and Marjorie Bicknell, editors: "A Primer for the Fibonacci Numbers", 1970, p. 87

Let P = the infinite lower triangular Pascal's Triangle matrix (A007318), and A = an array composed of bin(n,k; k=0,1,2)columns with alternating zeros.) Perform P * A and extract antidiagonals which become the rows of A106197.

Forming P * A, we get the following triangle (as a matrix, fill in the spaces with zeros):

1;

1, 1;

2, 2, 1;

4, 5, 3, 1;

8, 12, 9, 4, 1;

16, 28 25, 14, 5, 1;

32, 64, 66, 44, 20, 6, 1;

64, 144, 168, 129, 70, 27, 7, 1;

...

Cf. A045613, A006809, A062109.

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 24 2005

approved