The On-Line Encyclopedia of Integer Sequences (OEIS)

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A177978

Triangle T(n,k) read by rows: A051731(n,k) - A051731(n-1,k).
(history; published version)

#9 by Bruno Berselli at Tue Dec 17 05:34:14 EST 2019

STATUS

reviewed

approved

#8 by Michel Marcus at Tue Dec 17 05:33:01 EST 2019

STATUS

proposed

reviewed

#7 by Jon E. Schoenfield at Tue Dec 17 05:24:28 EST 2019

STATUS

editing

proposed

#6 by Jon E. Schoenfield at Tue Dec 17 05:24:22 EST 2019

NAME

Triangle T(n,k) read by rows: A051731(n,k) - A051731(n-1,k).

FORMULA

T(n,1)=A000007, k > 1: T(n,k) = (sum from Sum_{i = 1 to ..k-1 of } T(n-i,k-1)) - (sum from Sum_{i = 1 to ..k-1 of } T(n-i,k)).

EXAMPLE

1;

0.., 1;

0., -1.., 1;

0.., 1., -1.., 1;

0., -1.., 0., -1.., 1;

0.., 1.., 1.., 0., -1.., 1;

0., -1., -1.., 0.., 0., -1.., 1;

0.., 1.., 0.., 1.., 0.., 0., -1.., 1;

0., -1.., 1., -1.., 0.., 0.., 0., -1.., 1;

0.., 1., -1.., 0.., 1.., 0.., 0.., 0., -1.., 1;

0., -1.., 0.., 0., -1.., 0.., 0.., 0.., 0., -1.., 1;

0.., 1.., 1.., 1.., 0.., 1.., 0.., 0.., 0.., 0., -1.., 1;

0., -1., -1., -1.., 0., -1.., 0.., 0.., 0.., 0.., 0., -1.., 1;

0.., 1.., 0.., 0.., 0.., 0.., 1.., 0.., 0.., 0.., 0.., 0., -1.., 1;

STATUS

approved

editing

#5 by N. J. A. Sloane at Wed May 01 21:08:58 EDT 2013

EXTENSIONS

Typo in sequence (erroneous comma) corrected by _N. J. A. Sloane, _, May 22 2010

Discussion

Wed May 01

21:08

OEIS Server: https://oeis.org/edit/global/1898

#4 by Russ Cox at Fri Mar 30 18:53:10 EDT 2012

AUTHOR

_Mats Granvik (mats.granvik(AT)abo.fi), _, May 16 2010

EXTENSIONS

Edited by _Mats Granvik (mats.granvik(AT)abo.fi), _, Dec 11 2010

Discussion

Fri Mar 30

18:53

OEIS Server: https://oeis.org/edit/global/263

#3 by N. J. A. Sloane at Mon Dec 13 01:41:57 EST 2010

STATUS

proposed

approved

#2 by Mats Granvik at Sat Dec 11 11:26:45 EST 2010

COMMENTS

The recurrence for this triangle is similar to the recurrence in A177517. Cumulative column sums give table A051731.

FORMULA

T(n,1)=A000007, k>1: T(n,k) = (sum from i = 1 to k-1 of T(n-i,k-1)) - (sum from i = 1 to k-1 of T(n-i,k))

PROG

(Excel cell formula, American) =if(column()=1, if(row()>1, 0, 1), if(row()>=column(), sum(indirect(address(row()-column()+1, column()-1, 4)&":"&address(row()-1, column()-1, 4), 4))-sum(indirect(address(row()-column()+1, column(), 4)&":"&address(row()-1, column(), 4), 4)), 0))

(Excel cell formula, European)=if(column()=1; if(row()>1; 0; 1); if(row()>=column(); sum(indirect(address(row()-column()+1; column()-1; 4)&":"&address(row()-1; column()-1; 4); 4))-sum(indirect(address(row()-column()+1; column(); 4)&":"&address(row()-1; column(); 4); 4)); 0))

CROSSREFS

Matrix inverse of A134540. Cf. A177517.

EXTENSIONS

Edited by Mats Granvik (mats.granvik(AT)abo.fi), Dec 11 2010

STATUS

approved

proposed

#1 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010

NAME

Triangle T(n,k) read by rows: A051731(n,k)-A051731(n-1,k).

DATA

1, 0, 1, 0, -1, 1, 0, 1, -1, 1, 0, -1, 0, -1, 1, 0, 1, 1, 0, -1, 1, 0, -1, -1, 0, 0, -1, 1, 0, 1, 0, 1, 0, 0, -1, 1, 0, -1, 1, -1, 0, 0, 0, -1, 1, 0, 1, -1, 0, 1, 0, 0, 0, -1, 1, 0, -1, 0, 0, -1, 0, 0, 0, 0, -1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, -1, 1, 0, -1, -1, -1, 0, -1, 0, 0, 0, 0, 0, -1, 1, 0, 1

OFFSET

1,1

EXAMPLE

Triangle begins:

1

0..1

0.-1..1

0..1.-1..1

0.-1..0.-1..1

0..1..1..0.-1..1

0.-1.-1..0..0.-1..1

0..1..0..1..0..0.-1..1

0.-1..1.-1..0..0..0.-1..1

0..1.-1..0..1..0..0..0.-1..1

0.-1..0..0.-1..0..0..0..0.-1..1

0..1..1..1..0..1..0..0..0..0.-1..1

0.-1.-1.-1..0.-1..0..0..0..0..0.-1..1

0..1..0..0..0..0..1..0..0..0..0..0.-1..1

CROSSREFS

Matrix inverse of A134540.

KEYWORD

sign,tabl,new

AUTHOR

Mats Granvik (mats.granvik(AT)abo.fi), May 16 2010

EXTENSIONS

Typo in sequence (erroneous comma) corrected by N. J. A. Sloane, May 22 2010

STATUS

approved