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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A174014 Deleham triangle [1,1,-1,1,1,-1,1,...] DELTA [1,0,0,1,0,0,1,0,...], DELTA defined in A084938.

Original entry on oeis.org

1, 1, 1, 2, 3, 1, 3, 7, 5, 1, 4, 13, 15, 7, 1, 4, 19, 33, 26, 9, 1, 2, 19, 53, 66, 40, 11, 1, -3, 3, 51, 115, 115, 57, 13, 1, -10, -37, -19, 103, 215, 183, 77, 15, 1, -14, -89, -193, -120, 173, 364, 273, 100, 17, 1, -4, -91, -387, -664, -406, 252, 574, 388, 126, 19, 1
Offset: 0

Views

Author

Paul Barry, Mar 05 2010

Keywords

Comments

First column is A174015. Row sums are A174016. Diagonal sums are A174013.

Examples

			Triangle begins
1,
1, 1,
2, 3, 1,
3, 7, 5, 1,
4, 13, 15, 7, 1,
4, 19, 33, 26, 9, 1,
2, 19, 53, 66, 40, 11, 1,
-3, 3, 51, 115, 115, 57, 13, 1,
-10, -37, -19, 103, 215, 183, 77, 15, 1,
-14, -89, -193, -120, 173, 364, 273, 100, 17, 1
		

A174017 A (1,1) Somos-4 sequence.

Original entry on oeis.org

1, 2, -3, 1, 11, -16, -35, -129, 299, -386, -3977, 8063, 42489, 269344, -1000009, 3727745, 47166649, -123526014, -1764203419, -18228952703, 113727892147, -1065812586544, -18344075481339, 52130069331199, 2470319425874195
Offset: 0

Views

Author

Paul Barry, Mar 05 2010

Keywords

Comments

Hankel transform of A174013.

Programs

  • Magma
    I:=[1,2,-3,1]; [n le 4 select I[n] else (Self(n-1)*Self(n-3) + Self(n-2)^2)/Self(n-4): n in [1..30]]; // G. C. Greubel, Sep 18 2018
  • Mathematica
    RecurrenceTable[{a[n] == (a[n-1]*a[n-3] +a[n-2]^2)/a[n-4], a[0] == 1, a[1] == 2, a[2] == -3, a[3] == 1}, a, {n, 0, 150}] (* G. C. Greubel, Sep 18 2018 *)
    nxt[{a_,b_,c_,d_}]:={b,c,d,(b*d+c^2)/a}; NestList[nxt,{1,2,-3,1},30][[All,1]] (* Harvey P. Dale, Jun 21 2022 *)
  • PARI
    m=30; v=concat([1,2,-3,1], vector(m-4)); for(n=5, m, v[n] = ( v[n-1]*v[n-3] +v[n-2]^2)/v[n-4]); v \\ G. C. Greubel, Sep 18 2018
    

Formula

a(n) = (a(n-1)*a(n-3) + a(n-2)^2)/a(n-4), n>3.
Showing 1-2 of 2 results.