login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A177352 The triangle t(n,k) of the binomial sum as in A177351 in the column index range -floor(n/2)-1 <=k <= floor(n/2)-1. 0
1, 1, 2, 2, 1, 3, 3, 2, 5, 5, 5, 4, 1, 8, 8, 8, 7, 3, 13, 13, 13, 13, 12, 7, 1, 21, 21, 21, 21, 20, 14, 4, 34, 34, 34, 34, 34, 33, 26, 11, 1, 55, 55, 55, 55, 55, 54, 46, 25, 5, 89, 89, 89, 89, 89, 89, 88, 79, 51, 16, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Row sums are 1, 1, 5, 8, 20, 34, 72, 122, 241, 405, 769, 1284, 2375, 3947, 7165,

11866, 21238, 35078, 62094, 102340, 179561,.... which apparently is (n+1)*Fibonacci(n+1)- A129722(n) for even n, and n*Fibonacci(n+1)-A129722(n) for odd n.

The first column is A000045 by construction. The change in the column index range adds the Fibonacci numbers as a first column and removes the trailing zero in the rows compared to A177351.

Comment R. J. Mathar, Dec 20, 2010 (Start):

If we construct the complements of each row's entries with respect to the Fibonacci number of that row, an array

1;  # complement to 2

1,4;  # complement to 4,1

1,5   # complement to 7,3

1,6,12 # complement to 12,7,1

1,7,17 # complement to 20,14,4

1,8,23,33 # complement to 33,26,11,1

emerges which appears to be related to A038791. (End).

LINKS

Table of n, a(n) for n=0..60.

EXAMPLE

1

1;

2, 2, 1;

3, 3, 2;

5, 5, 5, 4, 1;

8, 8, 8, 7, 3;

13, 13, 13, 13, 12, 7, 1;

21, 21, 21, 21, 20, 14, 4;

34, 34, 34, 34, 34, 33, 26, 11, 1;

55, 55, 55, 55, 55, 54, 46, 25, 5;

89, 89, 89, 89, 89, 89, 88, 79, 51, 16, 1;

MATHEMATICA

w[n_, m_, k_] = Binomial[n - (m + k), m + k];

t[n_, k_] := Sum[w[n, m, k], {m, 1, Floor[n/2 - k]}];

Table[Table[t[n, k], {k, -Floor[n/2 + 1], Floor[n/2 + 1] - 2}], {n, 0,

   10}]

Flatten[%]

CROSSREFS

Cf. A177351, A000045

Sequence in context: A011373 A321783 A327035 * A210798 A117501 A117915

Adjacent sequences:  A177349 A177350 A177351 * A177353 A177354 A177355

KEYWORD

nonn,tabf

AUTHOR

Roger L. Bagula, Dec 10 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 19 00:18 EDT 2021. Contains 343098 sequences. (Running on oeis4.)