

A128229


A natural number transform, inverse of signed A094587.


16



1, 1, 1, 0, 2, 1, 0, 0, 3, 1, 0, 0, 0, 4, 1, 0, 0, 0, 0, 5, 1, 0, 0, 0, 0, 0, 6, 1, 0, 0, 0, 0, 0, 0, 7, 1, 0, 0, 0, 0, 0, 0, 0, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 9, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 1
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OFFSET

1,5


COMMENTS

Signed version of the transform (with 1, 2, 3, ... in the subdiagonal) gives A094587 having row sums A000522: (1, 2, 5, 16, 65, 236, ...). Unsigned inverse gives signed A094587 (with alternate signs); giving row sums = a signed variation of A094587 as follows: (1, 0, 1, 2, 9, 44, 265, 1854, ...). Binomial transform of the triangle = A093375.
Eigensequence of the triangle = A000085 starting (1, 2, 4, 10, 26, 76, ...).  Gary W. Adamson, Dec 29 2008


LINKS

Table of n, a(n) for n=1..91.


FORMULA

Infinite lower triangular matrix with (1,1,1,...) in the main diagonal and (1,2,3,...) in the subdiagonal.
T(n,n)=1, T(n,n1)=n1 and T(n,k)=0 for 1<=k<=n, 1<=n.  Hartmut F. W. Hoft, Jun 10 2017


EXAMPLE

First few rows of the triangle are:
1;
1, 1;
0, 2, 1;
0, 0, 3, 1;
0, 0, 0, 4, 1;
0, 0, 0, 0, 5, 1;
0, 0, 0, 0, 0, 6, 1;
0, 0, 0, 0, 0, 0, 7, 1;
...


MATHEMATICA

a128229[n_] := Table[Which[r==q, 1, r1==q, q, True, 0], {r, 1, n}, {q, 1, r}]
Flatten[a128229[13]] (* data *)
TableForm[a128229[8]] (* triangle *)
(* Hartmut F. W. Hoft, Jun 10 2017 *)


PROG

(Python)
def T(n, k): return 1 if n==k else n  1 if k==n  1 else 0
for n in range(1, 11): print [T(n, k) for k in range(1, n + 1)] # Indranil Ghosh, Jun 10 2017


CROSSREFS

Cf. A094587, A000522, A094587, A093375, A128228, A128227.
Cf. A000085.  Gary W. Adamson, Dec 29 2008
Sequence in context: A237053 A209777 A145677 * A132013 A105820 A136263
Adjacent sequences: A128226 A128227 A128228 * A128230 A128231 A128232


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, Feb 19 2007


STATUS

approved



