A131333 -id:A131333

Search: a131333 -id:a131333

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A131332

Triangle read by rows: A065941 * A097807.

+10
5

1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 2, -1, 2, 1, 1, 3, -2, 3, 1, 2, 1, 5, -4, 5, 0, 4, 2, 1, 8, -7, 8, -2, 7, 3, 3, 1, 13, -12, 13, -6, 12, 3, 7, 3, 1, 21, -20, 21, -13, 20, 1, 14, 6, 4, 1, 34, -33, 34, -25, 33, -5, 26, 9, 11, 4, 1, 55, -54, 55, -45, 54, -18, 46, 10, 25, 10, 5, 1, 89, -88, 89, -78, 88, -43, 79, 5, 51, 19, 16, 5, 1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,11

COMMENTS

Row sums = Fibonacci numbers: (1, 1, 2, 3, 5, 8, ...).

LINKS

Table of n, a(n) for n=1..91.

FORMULA

A065941 * A000012(signed by columns, + - + - ...).

EXAMPLE

First few rows of the triangle are:

0, 1;

1, 0, 1;

1, 0, 1, 1;

2, -1, 2, 1, 1;

3, -2, 3, 1, 2, 1;

5, -4, 5, 0, 4, 2, 1;

8, -7, 8, -2, 7, 3, 3, 1;

...

CROSSREFS

Cf. A097807, A131333, A131334, A131335, A131336.

KEYWORD

tabl,sign

AUTHOR

Gary W. Adamson, Jun 29 2007

EXTENSIONS

a(47) = -20 corrected, name edited and more terms from Georg Fischer, Jun 05 2023

STATUS

approved

A131334

A000012(signed) * A065941.

+10
5

1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 2, 1, 1, 0, 1, 2, 2, 2, 1, 1, 0, 3, 2, 4, 2, 1, 0, 1, 3, 3, 6, 4, 3, 1, 1, 0, 4, 3, 9, 6, 7, 3, 1, 0, 1, 4, 4, 12, 9, 13, 7, 4, 1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,13

COMMENTS

Row sums = Fibonacci numbers.

LINKS

Table of n, a(n) for n=1..55.

FORMULA

A000012(signed by columns, + - + -...) * A065941.

EXAMPLE

First few rows of the triangle are:

0, 1;

1, 0, 1;

0, 1, 1, 1;

1, 0, 2, 1, 1;

0, 1, 2, 2, 2, 1;

1, 0, 3, 2, 4, 2, 1;

0, 1, 3, 3, 6, 4, 3, 1;

1, 0, 4, 3, 9, 6, 7, 3, 1;

...

CROSSREFS

Cf. A131332, A131333, A131335, A131336.

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Jun 29 2007

STATUS

approved

A131335

A000012 * A131334.

+10
5

1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 3, 2, 4, 2, 1, 3, 3, 6, 4, 3, 1, 4, 3, 9, 6, 7, 3, 1, 4, 4, 12, 9, 13, 7, 4, 1, 5, 4, 16, 12, 22, 13, 11, 4, 1, 5, 5, 20, 16, 34, 22, 24, 11, 5, 1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,4

COMMENTS

Row sums = A000071, Fibonacci numbers - 1, starting (1, 2, 4, 7, 12, 20, 33,...).

LINKS

Table of n, a(n) for n=1..55.

FORMULA

A000012 * A131334 as infinite lower triangular matrices, where A000012 = (1; 1,1; 1,1,1;...).

EXAMPLE

First few rows of the triangle are:

1, 1;

2, 1, 1;

2, 2, 2, 1;

3, 2, 4, 2, 1;

3, 3, 6, 4, 3, 1;

4, 3, 9, 6, 7, 3, 1;

...

CROSSREFS

Cf. A000071, A131334, A000012, A131332, A131333.

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Jun 29 2007

STATUS

approved

A131336

A131334 * A000012.

+10
4

1, 1, 1, 2, 1, 1, 3, 3, 2, 1, 5, 4, 4, 2, 1, 8, 8, 7, 5, 3, 1, 13, 12, 12, 9, 7, 3, 1, 21, 21, 20, 17, 14, 8, 4, 1, 34, 33, 33, 29, 26, 17, 11, 4, 1, 55, 55, 54, 50, 46, 34, 25, 12, 5, 1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,4

COMMENTS

Left border = Fibonacci numbers. Row sums = A131337.

LINKS

Table of n, a(n) for n=1..55.

FORMULA

A131334 * A000012, (partial row sums of A131334 starting from the right).

EXAMPLE

First few rows of the triangle are:

1, 1;

2, 1, 1;

3, 3, 2, 1;

5, 4, 4, 2, 1;

8, 8, 7, 5, 3, 1;

13, 12, 12, 9, 7, 3, 1;

21, 21, 20 17, 14, 8, 4, 1;

...

CROSSREFS

Cf. A131334, A131332, A131333, A131335, A131337.

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Jun 29 2007

STATUS

approved

A131337

Row sums of triangle A131336.

+10
1

1, 2, 4, 9, 16, 32, 57, 106, 188, 337

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..10.

EXAMPLE

a(4) = 9 = (3 + 3 + 2 + 2), sum of row 4, A131336.

CROSSREFS

Cf. A131332, A131333, A131334, A131335, A131336.

KEYWORD

nonn

AUTHOR

Gary W. Adamson, Jun 29 2007

STATUS

approved

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