A103455 -id:A103455 - cp's OEIS frontend

A103452 Inverse of number triangle A103451.

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

Offset: 0

Paul Barry, Feb 06 2005

Triangle T(n,k), 0 <= k <= n, read by rows given by [ -1, 2, 0, 0, 0, 0, 0, ...] DELTA [1, 0, -1/2, 1/2, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938. - Philippe Deléham, May 01 2007

			Triangle begins
   1;
  -1, 1;
  -1, 0, 1;
  -1, 0, 0, 1;
  -1, 0, 0, 0, 1;
  -1, 0, 0, 0, 0, 1;
  -1, 0, 0, 0, 0, 0, 1;
  -1, 0, 0, 0, 0, 0, 0, 1;
  -1, 0, 0, 0, 0, 0, 0, 0, 1;
  -1, 0, 0, 0, 0, 0, 0, 0, 0, 1;
  -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
Production matrix begins
  -1, 1;
  -2, 1, 1;
  -2, 1, 0, 1;
  -2, 1, 0, 0, 1;
  -2, 1, 0, 0, 0, 1;
  -2, 1, 0, 0, 0, 0, 1;
  -2, 1, 0, 0, 0, 0, 0, 1;
  -2, 1, 0, 0, 0, 0, 0, 0, 1;

Michael De Vlieger, Table of n, a(n) for n = 0..10010 (Rows 0 <= n <= 140)

Cf. A000007 (row sums), A103453, A103454, A103455.

Table[Range[n] /. {k_ /; k == 1 && n != 1 -> -1, k_ /; k == n -> 1, Integer -> 0}, {n, 15}] // Flatten (* _Michael De Vlieger, Jul 21 2016 *)

flatten([[1 if k==n else -1 if k==0 else 0 for k in (0..n)] for n in (0..15)]) # G. C. Greubel, Jun 18 2021

T(n,k) = 1 if k = n, -1 if k = 0, otherwise 0.
Sum_{k=0..n} T(n, k) = 0^n (row sums).
Sum_{k=0..floor(n/2)} T(n-k, k) = 0^n - (1-(-1)^n)/2 (diagonal sums).
G.f.: (1 - 2*x + y*x^2)/((1-x)*(1-y*x)). - Philippe Deléham, Feb 11 2012

A114808 The numbers 5^n-1 written in groups of three digits, with leading zeros omitted.

Original entry on oeis.org

424, 124, 624, 312, 415, 624, 781, 243, 906, 241, 953, 124, 976, 562, 448, 828, 124, 244, 140, 624, 122, 70, 312, 461, 35, 156, 243, 51, 757, 812, 415, 258, 789, 62, 476, 293, 945, 312, 438, 146, 972, 656, 241, 907, 348, 632, 812, 495, 367, 431, 640, 624, 476, 837, 158, 203, 124, 238, 418, 579

Offset: 1

Jonathan Vos Post, Feb 19 2006

			4, 24, 124, 624, 3124, 15624, ...

Cf. A024049, A103455, A114645.

L := [] ;
for n from 1 to 30 do
    dggs := ListTools[Reverse](convert(5^n-1,base,10) );
    L := [op(L),op(dggs)] ;
end do:
for k from 1 to nops(L)-3 by 3 do
    op(k,L)*100+op(k+1,L)*10+op(k+2,L) ;
    printf("%d,",%) ;
end do: # R. J. Mathar, Jun 23 2014

FromDigits[#] & /@ Partition[ Flatten@ IntegerDigits@ Table[5^n - 1, {n, 22}], 3] (* Robert G. Wilson v, Jun 23 2014 *)

Definition and terms realigned with A114645 by Robert G. Wilson v, Jun 23 2014

cp's OEIS Frontend

A103452 Inverse of number triangle A103451.

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