A128541 -id:A128541 - cp's OEIS frontend

A128585 Triangle read by rows: A007318^(-1) * A128541.

1, 0, 1, -1, -1, 2, 2, 0, -4, 3, -3, 2, 4, -9, 5, 4, -5, 0, 15, -20, 8, -5, 9, -10, -15, 45, -40, 13, 6, -14, 28, 0, -70, 112, -78, 21, -7, 20, -56, 42, 70, -224, 260, -147, 34, 8, -27, 96, -126, 0, 336, -624, 567, -272, 55, -9, 35, -150, 270, -210, -336, 1170, -1575, 1190, -495, 89

Offset: 1

Gary W. Adamson, Mar 11 2007

Row sums = A039834: (1, 1, 0, -1, 2, -3, 5, -8, ...); binomial transform of A039834 = (1, 2, 3, 5, 8, 13, 21, ...).

			First few rows of the triangle
   1;
   0,   1;
  -1,  -1,   2;
   2,   0,  -4,   3;
  -3,   2,   4,  -9,   5;
   4,  -5,   0,  15, -20,   8;
  ...

Cf. A007318, A039834, A128541, A130595.

Inverse binomial transform of A128541.

Matrix product A130595 * A128541. - Georg Fischer, Jun 01 2023

a(35) corrected and more terms from Georg Fischer, Jun 01 2023

A128540 Triangle A127647 * A097806, read by rows.

Original entry on oeis.org

1, 1, 1, 0, 2, 2, 0, 0, 3, 3, 0, 0, 0, 5, 5, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 13, 13, 0, 0, 0, 0, 0, 0, 21, 21, 0, 0, 0, 0, 0, 0, 0, 34, 34, 0, 0, 0, 0, 0, 0, 0, 0, 55, 55, 0, 0, 0, 0, 0, 0, 0, 0, 0, 89, 89, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, 144

Offset: 1

Gary W. Adamson, Mar 10 2007

Row sums = A094895 starting (1, 2, 4, 6, 10, 16, 26, ...). A128541 = A097806 * A127647.

			First few rows of the triangle:
  1;
  1, 1;
  0, 2, 2;
  0, 0, 3, 3;
  0, 0, 0, 5, 5;
  0, 0, 0, 0, 8, 8;
  ...

G. C. Greubel, Rows n = 1..100 of triangle, flattened

Cf. A127647, A097806, A128541.

[k eq n select Fibonacci(n) else k eq n-1 select Fibonacci(n) else 0: k in [1..n], n in [1..15]]; // G. C. Greubel, Jul 11 2019

Table[If[k==n || k==n-1, Fibonacci[n], 0], {n, 15}, {k, n}]//Flatten (* G. C. Greubel, Jul 11 2019 *)

T(n,k) = if(k==n || k==n-1, fibonacci(n), 0); \\ G. C. Greubel, Jul 11 2019

def T(n, k):
    if (k==n): return fibonacci(n)
    elif (k==n-1): return fibonacci(n)
    else: return 0
[[T(n, k) for k in (1..n)] for n in (1..15)] # G. C. Greubel, Jul 11 2019

A127646 * A097806 as infinite lower triangular matrices.

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A128585 Triangle read by rows: A007318^(-1) * A128541.

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A128540 Triangle A127647 * A097806, read by rows.

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