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 1-2 of 2 results.

A232806 a(n) = a(n-1)^2/2 + 5/2, a(0) = 1.

Original entry on oeis.org

1, 3, 7, 27, 367, 67347, 2267809207, 2571479299676984427, 3306252894333617140505030630200259167
Offset: 0

Views

Author

Richard R. Forberg, Nov 30 2013

Keywords

Comments

First differences are 2*A063573.

Crossrefs

Cf. A063573, A002065, A166105.

Formula

a(n) = 2*A002065(n) + 1.
a(n) = 2*A166105(n) - 1. - Robert FERREOL, May 31 2020
a(n) = A002065(n) + A166105(n). - Alois P. Heinz, Jun 07 2020

A294082 Square array read by antidiagonals: T(m,n) = T(m,n-1)^2 - T(m,n-2)^2 + T(m,n-2) with T(1,n) = 1, T(m,0) = 1, and T(m,1) = m.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 14, 9, 4, 1, 1, 184, 75, 16, 5, 1, 1, 33674, 5553, 244, 25, 6, 1, 1, 1133904604, 30830259, 59296, 605, 36, 7, 1, 1, 1285739649838492214, 950504839176825, 3515956324, 365425, 1266, 49, 8, 1
Offset: 1

Views

Author

David M. Cerna, Feb 09 2018

Keywords

Comments

The columns of T(n,m) enumerate the size of the set S(n) constructed recursively as follows: Let S(1) = {a_1, ..., a_m}, where a_i are arbitrary elements, and let P(S) be the set of pairs (s,t) where s,t are members of S and s is not equal to t. We define S(n+1) to be the union of S(n) and P(S(n)). For example Let S(1) = {a_1,a_2}, then S(2) = {a_1,a_2, (a_1,a_2),(a_2,a_1)} where (a_1,a_2) is the pairing of a_{1} and a_{2}. Furthermore S(2) = {a_1,a_2, (a_1,a_2),(a_2,a_1), (a_1,(a_1,a_2)), (a_1,(a_2,a_1)), ((a_1,a_2),a_1), ((a_2,a_1),a_1), (a_2,(a_1,a_2)), (a_2,(a_2,a_1)), ((a_1,a_2),a_2), ((a_2,a_1),a_2)((a_1,a_2), (a_2,a_1)) }.

Examples

			Array begins:
=============================================================================
m\n| 0  1   2     3         4                5                              6
---|-------------------------------------------------------------------------
1  | 1  1   1     1         1                1                              1
2  | 1  2   4    14       184            33674                     1133904604
3  | 1  3   9    75      5553         30830259                950504839176825
4  | 1  4  16   244     59296       3515956324           12361948868759636656
5  | 1  5  25   605    365425     133535065205        17831613639170066626825
6  | 1  6  36  1266   1601496    2564787836526      6578136646389154911912156
7  | 1  7  49  2359   5562529   30941723313319    957390241597957573719482449
8  | 1  8  64  4040  16317568  266263009117064  70895990024073440521846863040
  ...

Crossrefs

Cf. A000058, A166105.

Programs

  • Mathematica
    t[n_, m_] := t[n -1, m]^2 - t[n -2, m]^2 + t[n -2, m]; t[0, m_] := 1; t[1, m_] := m; Table[ t[n -m +1, m], {n, 0, 8}, {m, n +1}] // Flatten
(* to produce the table *) Table[t[n, m], {m, 8}, {n, 0, 6}] // TableForm (* Robert G. Wilson v, Feb 09 2018 *)
  • PARI
    T(n, k) = if (k<0, 0, if (n==1, 1, if (k==0, 1, if (k==1, n, T(n, k-1)^2 - T(n, k-2)^2 + T(n, k-2)))));
tabl(nn) = for (n=1, nn , for (k=0, nn, print1(T(n, k), ", ")); print); \\ Michel Marcus, Mar 06 2018
Showing 1-2 of 2 results.

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

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