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.

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A193998 Mirror of the triangle A193997.

Original entry on oeis.org

1, 3, 2, 6, 8, 3, 11, 23, 18, 5, 19, 55, 66, 37, 8, 32, 120, 196, 167, 73, 13, 53, 246, 511, 587, 388, 139, 21, 87, 484, 1225, 1777, 1578, 853, 259, 34, 142, 924, 2765, 4857, 5428, 3933, 1799, 474, 55, 231, 1725, 5969, 12333, 16642, 15147, 9275, 3678
Offset: 0

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Author

Clark Kimberling, Aug 11 2011

Keywords

Comments

A193998 is obtained by reversing the rows of the triangle A193997.

Examples

			First six rows:
1
3....2
6....8.....3
11...23....18....5
19...55....66....37....8
32...120...196...167...73...13
		

Crossrefs

Cf. A193997.

Programs

  • Mathematica
    z = 11;
    p[n_, x_] := Sum[Fibonacci[k + 1]*x^(n - k), {k, 0, n}];
    q[n_, x_] := (x + 1)^n;
    p1[n_, k_] := Coefficient[p[n, x], x^k];
    p1[n_, 0] := p[n, x] /. x -> 0;
    d[n_, x_] := Sum[p1[n, k]*q[n - 1 - k, x], {k, 0, n - 1}]
    h[n_] := CoefficientList[d[n, x], {x}]
    TableForm[Table[Reverse[h[n]], {n, 0, z}]]
    Flatten[Table[Reverse[h[n]], {n, -1, z}]]  (* A193997 *)
    TableForm[Table[h[n], {n, 0, z}]]
    Flatten[Table[h[n], {n, -1, z}]]  (* A193998 *)

Formula

Write w(n,k) for the triangle at A193997. The triangle at A193998 is then given by w(n,n-k).
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