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!)
A156628 Square array, read by antidiagonals, where row n+1 is generated from row n by first removing terms in row n at positions 0 and {(m+1)*(m+2)/2-2, m>0} and then taking partial sums, starting with all 1's in row 0. 2
1, 1, 1, 3, 2, 1, 13, 7, 3, 1, 71, 33, 13, 4, 1, 461, 191, 71, 20, 5, 1, 3447, 1297, 461, 120, 28, 6, 1, 29093, 10063, 3447, 836, 181, 38, 7, 1, 273343, 87669, 29093, 6616, 1333, 270, 49, 8, 1, 2829325, 847015, 273343, 58576, 11029, 2150, 375, 61, 9, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..54.

FORMULA

Column 0 = Column 0 of triangle A104980 = A003319.

Column 1 = Column 1 of triangle A104980 = A104981.

Column 3 = column 1 of A104988 (matrix square of A104980).

Column 5 = column 2 of A104988 (matrix square of A104980).

EXAMPLE

To generate the array, start with all 1's in row 0; from then on,

obtain row n+1 from row n by first removing terms in row n at

positions 0 and {(m+1)*(m+2)/2-2,m>0} and then taking partial sums.

This square array A begins:

(1), (1), 1, 1, (1), 1, 1, 1, (1), 1, 1, 1, 1, (1), 1, 1, 1, 1, 1, ...;

(1), (2), 3, 4, (5), 6, 7, 8, (9), 10, 11, 12, 13, (14), 15, 16, ...;

(3), (7), 13, 20, (28), 38, 49, 61, (74), 89, 105, 122, 140, (159),...;

(13), (33), 71, 120, (181), 270, 375, 497, (637), 817, 1019, 1244, ...;

(71), (191), 461, 836, (1333), 2150, 3169, 4413, (5906), 8001, ...;

(461), (1297), 3447, 6616, (11029), 19030, 29483, 42775, (59324),...;

(3447), (10063), 29093, 58576, (101351), 185674, 300329, 451277, ...;

(29093), (87669), 273343, 573672, (1024949), 1982310, 3330651, ...;

(273343), (847015), 2829325, 6159976, (11320359), 23009602, 39998897, ...;

where terms in parenthesis at positions {0,1,4,8,13,..} in a row

are removed before taking partial sums to obtain the next row.

...

RELATION TO SPECIAL TRIANGLE.

Triangle A104980 begins:

1;

1, 1;

3, 2, 1;

13, 7, 3, 1;

71, 33, 13, 4, 1;

461, 191, 71, 21, 5, 1;

3447, 1297, 461, 133, 31, 6, 1;

29093, 10063, 3447, 977, 225, 43, 7, 1; ...

in which column 0 and column 1 are found in square array A.

...

Matrix square of A104980 = triangle A104988 which begins:

1;

2, 1;

8, 4, 1;

42, 20, 6, 1;

266, 120, 38, 8, 1;

1954, 836, 270, 62, 10, 1;

16270, 6616, 2150, 516, 92, 12, 1;

151218, 58576, 19030, 4688, 882, 128, 14, 1; ...

where column 1 and column 2 are also found in square array A.

PROG

(PARI) {T (n, k)=local (A=0, b=2, c=1, d=0); if (n==0, A=1, until (d>k, if (c==b* (b+1)/2-2, b+=1, A+=T (n-1, c); d+=1); c+=1)); A}

CROSSREFS

Cf. columns: A003319, A104981, A156629, related triangles: A104980, A104988.

Cf. related tables: A136212, A136213, A125714, A135876, A127054, A125781, A136217.

Sequence in context: A048647 A180190 A059438 * A104980 A316566 A134090

Adjacent sequences:  A156625 A156626 A156627 * A156629 A156630 A156631

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Feb 17 2009

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 August 3 17:04 EDT 2021. Contains 346439 sequences. (Running on oeis4.)