The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A067337 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing all changes.

A067337

Triangle where T(n,k)=2*T(n,k-1)+C(n-1,k)-C(n-1,k-1) and n>=k>=0.
(history; published version)

#4 by Russ Cox at Fri Mar 30 18:51:35 EDT 2012

AUTHOR

_Henry Bottomley (se16(AT)btinternet.com), _, Jan 15 2002

Discussion

Fri Mar 30

18:51

OEIS Server: https://oeis.org/edit/global/247

#3 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

CROSSREFS

Row sums are A025192. Columns include A000012, A000027, and A022856 (essentially). Right hand columns include A000244 (essentially), A007051, and A047926. Central diagonal is A067336.

KEYWORD

nonn,tabl,new

#2 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006

FORMULA

T(n, k)=2*T(n, k-1)+A037012(n, k). T(n, k)=T(n-1, k-1)+T(n-1, k) if k<n. T(n, n)=Sum_{j<n}T(n, j)=3^(n-1) if n>0.

KEYWORD

nonn,tabl,new

#1 by N. J. A. Sloane at Fri May 16 03:00:00 EDT 2003

NAME

Triangle where T(n,k)=2*T(n,k-1)+C(n-1,k)-C(n-1,k-1) and n>=k>=0.

DATA

1, 1, 1, 1, 2, 3, 1, 3, 5, 9, 1, 4, 8, 14, 27, 1, 5, 12, 22, 41, 81, 1, 6, 17, 34, 63, 122, 243, 1, 7, 23, 51, 97, 185, 365, 729, 1, 8, 30, 74, 148, 282, 550, 1094, 2187, 1, 9, 38, 104, 222, 430, 832, 1644, 3281, 6561, 1, 10, 47, 142, 326, 652, 1262, 2476, 4925, 9842

OFFSET

0,5

FORMULA

T(n,k)=2*T(n,k-1)+A037012(n,k). T(n,k)=T(n-1,k-1)+T(n-1,k) if k<n. T(n,n)=Sum_{j<n}T(n,j)=3^(n-1) if n>0.

EXAMPLE

Rows start 1; 1,1; 1,2,3; 1,3,5,9; 1,4,8,14,27; etc. T(4,0)=2*0+1-0=1; T(4,1)=2*1+3-1=4; T(4,2)=2*4+3-3=8; T(4,3)=2*8+1-3=14; T(4,4)=2*14+0-1=27.

CROSSREFS

Row sums are A025192. Columns include A000012, A000027, and A022856 (essentially). Right hand columns include A000244 (essentially), A007051, and A047926. Central diagonal is A067336.

KEYWORD

nonn,tabl

AUTHOR

Henry Bottomley (se16(AT)btinternet.com), Jan 15 2002

STATUS

approved