OFFSET
1,3
COMMENTS
FORMULA
T(d,n)=T(d-1,n+1)-T(d-1,n). T(0,n)=A001045(n).
Row sums: sum_{n=0..d-1} T(d,n) = A002450([(d+1)/2]).
Row sums of absolute values: sum_{n=0..d-1} |T(d,n)| = A045883(d).
T(d,n) = (2^n - 2^d*(-1)^(d+n))/3, for d > n >= 0. - Jianing Song, Aug 11 2022
EXAMPLE
A001045 and its d times iterated differences are
.0,.1,.1,.3,.5,11,21,43,...
.1,.0,.2,.2,.6,10,22,... < d=1
-1,.2,.0,.4,.4,12,... < d=2
.3,-2,.4,.0,.8,.. < d=3
-5,.6,-4,.8,.0,...
The sequence contains the first d elements of the d-th row, those up to the diagonal (which contains zeros).
PROG
(PARI) T(d, n) = (2^n - 2^d*(-1)^(d+n))/3 \\ Jianing Song, Aug 11 2022
CROSSREFS
KEYWORD
AUTHOR
Paul Curtz, Jun 30 2008
EXTENSIONS
Edited by R. J. Mathar, Jul 14 2008
STATUS
approved