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.

A172430 Period length 10: repeat 2,1,6,7,0,3,4,9,8,5 .

Original entry on oeis.org

2, 1, 6, 7, 0, 3, 4, 9, 8, 5, 2, 1, 6, 7, 0, 3, 4, 9, 8, 5, 2, 1, 6, 7, 0, 3, 4, 9, 8, 5, 2, 1, 6, 7, 0, 3, 4, 9, 8, 5, 2, 1, 6, 7, 0, 3, 4, 9, 8, 5, 2, 1, 6, 7, 0, 3, 4, 9, 8, 5, 2, 1, 6, 7, 0, 3, 4, 9, 8, 5, 2, 1, 6, 7, 0, 3, 4, 9, 8, 5, 2, 1, 6, 7, 0, 3, 4, 9, 8, 5, 2, 1, 6, 7, 0, 3, 4, 9, 8, 5, 2, 1, 6, 7, 0, 3
Offset: 0

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Author

Paul Curtz, Feb 02 2010

Keywords

Comments

Also the decimal expansion of the rational number 240781665 / 1111111111 .

Formula

a(n) = A172285(n+1) mod 10.
G.f.: (2+x+6*x^2+7*x^3+3*x^5+4*x^6+9*x^7+8*x^8+5*x^9)/ ((1-x) * (1+x) * (x^4+x^3+x^2 +x+1)* (x^4-x^3+x^2-x+1)).
a(3*n) = A172423(n+2).

Extensions

Edited by R. J. Mathar, Feb 11 2010

A172416 a(n) = 5*2^n/9 + 1/4 + (-1)^n*(n/6 + 7/36).

Original entry on oeis.org

1, 1, 3, 4, 10, 17, 37, 70, 144, 283, 571, 1136, 2278, 4549, 9105, 18202, 36412, 72815, 145639, 291268, 582546, 1165081, 2330173, 4660334, 9320680, 18641347, 37282707, 74565400, 149130814, 298261613, 596523241
Offset: 0

Views

Author

Paul Curtz, Feb 02 2010

Keywords

Comments

The sequence and the 1st, 2nd, 3rd etc. difference form the array
1, 1, 3, 4, 10, 17, 37, 70, 144, 283, 571, 1136,..
0, 2, 1, 6, 7, 20, 33, 74, 139, 288, 565, 1142, 2271,..
2, -1, 5, 1, 13, 13, 41, 65, 149, 277, 577, 1129, 2285,..
-3, 6, -4, 12, 0, 28, 24, 84, 128, 300, 552, 1156,...
where the sequence 1,2,5,12,.... = A045623 appears on the diagonal.

Links

Programs

  • Magma
    [5*2^n/9 +1/4 +(-1)^n*(n/6+7/36): n in [0..40]]; // Vincenzo Librandi, Aug 05 2011

Formula

a(n) = a(n-1) + 3*a(n-2) - a(n-3) - 2*a(n-4).
a(n+1) - a(n) = A172285(n).
a(2n) = A164044(n).
a(2n+1) = A172447(n).
a(n+1) - 2*a(n) = (-1)^(n+1)*A008619(n).
G.f.: ( 1 - x^2 - x^3 ) / ( (2*x-1)*(x-1)*(1+x)^2 ).
Showing 1-2 of 2 results.

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

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