cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A128586 Triangle read by rows: A007318^(-1) * A128540.

Original entry on oeis.org

1, 0, 1, -1, 0, 2, 2, -3, -3, 3, -3, 8, 0, -7, 5, 4, -15, 10, 5, -17, 8, -5, 24, -30, 15, 27, -35, 13, 6, -35, 63, -70, -7, 77, -70, 21, -7, 48, -112, 182, -98, -84, 196, -134, 34, 8, -63, 180, -378, 378, -84, -336, 450, -251, 55, -9, 80, -270, 690, -966, 714, 210, -990, 980, -461, 89
Offset: 1

Views

Author

Gary W. Adamson, Mar 11 2007

Keywords

Comments

Row sums = A128587: (1, 1, 1, -1, 3, -5, 9, -15, 25, -41, ...).

Examples

			First few rows of the triangle:
   1;
   0,   1;
  -1,   0,   2;
   2,  -3,  -3,   3;
  -3,   8,   0,  -7,   5;
   4, -15,  10,   5, -17,   8;
  ...

Crossrefs

Cf. A007318, A128540, A128587, A128588, A130595.

Formula

Inverse binomial transform of A128540.
Matrix product A130595 * A128540. - Georg Fischer, Jun 01 2023

Extensions

a(33) corrected, a(42)=-84 inserted and more terms from Georg Fischer, Jun 01 2023

A128544 A007318 * A128540.

Original entry on oeis.org

1, 2, 1, 3, 4, 2, 4, 9, 9, 3, 5, 16, 24, 17, 5, 6, 25, 50, 55, 33, 8, 7, 36, 90, 135, 123, 61, 13, 8, 49, 147, 280, 343, 259, 112, 21, 9, 64, 224, 518, 798, 812, 532, 202, 34, 10, 81, 324, 882, 1638, 2100, 1848, 1062, 361, 55
Offset: 0

Views

Author

Gary W. Adamson, Mar 10 2007

Keywords

Comments

Row sums = A069403: (1, 3, 9, 25, 67, ...).

Examples

			First few rows of the triangle:
  1;
  2,  1;
  3,  4,  2;
  4,  9,  9,   3;
  5, 16, 24,  17,   5;
  6, 25, 50,  55,  33,  8;
  7, 36, 90, 135, 123, 61, 13;
  ...

Crossrefs

Cf. A007318, A128540, A069403.

Formula

A007318 * A128540 as infinite lower triangular matrices; (binomial transform of A128540).

A128541 Triangle, A097806 * A127647, read by rows.

Original entry on oeis.org

1, 1, 1, 0, 1, 2, 0, 0, 2, 3, 0, 0, 0, 3, 5, 0, 0, 0, 0, 5, 8, 0, 0, 0, 0, 0, 8, 13, 0, 0, 0, 0, 0, 0, 13, 21, 0, 0, 0, 0, 0, 0, 0, 21, 34, 0, 0, 0, 0, 0, 0, 0, 0, 34, 55, 0, 0, 0, 0, 0, 0, 0, 0, 0, 55, 89, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 89, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, 233
Offset: 0

Views

Author

Gary W. Adamson, Mar 10 2007

Keywords

Comments

Row sums = A000045 starting (1, 2, 3, 5, 8, 13, ...). A128540 = A127647 * A097806.

Examples

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

Links

Crossrefs

Cf. A000045, A097806, A127647, A128540.

Programs

  • Magma
    [k eq n select Fibonacci(n+1) else k eq n-1 select Fibonacci(n) else 0: k in [0..n], n in [0..15]]; // G. C. Greubel, Jul 11 2019
  • Mathematica
    Table[If[k==n, Fibonacci[n+1], If[k==n-1, Fibonacci[n], 0]], {n, 0, 15}, {k, 0, n}]//Flatten (* G. C. Greubel, Jul 11 2019 *)
  • PARI
    T(n,k) = if(k==n, fibonacci(n+1), if(k==n-1, fibonacci(n), 0)); \\ G. C. Greubel, Jul 11 2019
  • Sage
    def T(n, k):
    if (k==n): return fibonacci(n+1)
    elif (k==n-1): return fibonacci(n)
    else: return 0
[[T(n, k) for k in (0..n)] for n in (0..15)] # G. C. Greubel, Jul 11 2019

Formula

A097806 * A127647 as infinite lower triangular matrices.

Extensions

More terms added by G. C. Greubel, Jul 11 2019
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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