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.

A064650 a(n) = floor(a(n-1)/2) + a(n-2) with a(0)=1, a(1)=2.

Original entry on oeis.org

1, 2, 2, 3, 3, 4, 5, 6, 8, 10, 13, 16, 21, 26, 34, 43, 55, 70, 90, 115, 147, 188, 241, 308, 395, 505, 647, 828, 1061, 1358, 1740, 2228, 2854, 3655, 4681, 5995, 7678, 9834, 12595, 16131, 20660, 26461, 33890, 43406, 55593, 71202, 91194, 116799, 149593, 191595
Offset: 0

Views

Author

Henry Bottomley, Oct 04 2001

Keywords

Comments

a(n)/a(n-1) tends to (1+sqrt(17))/4 = 1.2807764...

Crossrefs

Programs

  • Haskell
    a064650 n = a064650_list !! n
    a064650_list = 1 : 2 : zipWith (+)
                           a064650_list (map (flip div 2) $ tail a064650_list)
    -- Reinhard Zumkeller, Apr 30 2015
  • Magma
    [n le 2 select n else Floor(Self(n-1)/2)+Self(n-2): n in [1..50]]; // Bruno Berselli, Apr 21 2012
    
  • Mathematica
    RecurrenceTable[{a[0] == 1, a[1] == 2, a[n] == Floor[a[n - 1]/4] + a[n - 2]}, a, {n, 49}] (* Bruno Berselli, Apr 21 2012 *)
  • PARI
    { for (n=0, 400, if (n>1, a=a1\2 + a2; a2=a1; a1=a, if (n, a=a1=2, a=a2=1)); write("b064650.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 21 2009
    

Formula

a(n) = A064651(n) + 1.

A182229 a(n) = a(n-1) + floor(a(n-2)/3) with a(0)=2, a(1)=3.

Original entry on oeis.org

2, 3, 3, 4, 5, 6, 7, 9, 11, 14, 17, 21, 26, 33, 41, 52, 65, 82, 103, 130, 164, 207, 261, 330, 417, 527, 666, 841, 1063, 1343, 1697, 2144, 2709, 3423, 4326, 5467, 6909, 8731, 11034, 13944, 17622, 22270, 28144, 35567, 44948, 56803, 71785, 90719, 114647, 144886, 183101
Offset: 0

Views

Author

Alex Ratushnyak, Apr 19 2012

Keywords

Comments

a(n)/a(n-1) tends to (3+sqrt(21))/6 = 1.263762615825973334... [Bruno Berselli, Apr 23 2012]

Crossrefs

Programs

  • Haskell
    a182229 n = a182229_list !! n
    a182229_list = 2 : 3 : zipWith (+)
                           (map (flip div 3) a182229_list) (tail a182229_list)
    -- Reinhard Zumkeller, Apr 30 2015
  • Magma
    [n le 2 select n+1 else Self(n-1)+Floor(Self(n-2)/3): n in [1..51]]; // Bruno Berselli, Apr 21 2012
    
  • Mathematica
    RecurrenceTable[{a[0] == 2, a[1] == 3, a[n] == a[n - 1] + Floor[a[n - 2]/3]}, a, {n, 50}] (* Bruno Berselli, Apr 21 2012 *)
  • Python
    prpr = 2
    prev = 3
    for i in range(2,51):
        current = prev + prpr//3
        print(current, end=',')
        prpr = prev
        prev = current
    

A182280 a(n) = floor(a(n-1)/4)+a(n-2) with a(0)=3, a(1)=4.

Original entry on oeis.org

3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 9, 10, 11, 12, 14, 15, 17, 19, 21, 24, 27, 30, 34, 38, 43, 48, 55, 61, 70, 78, 89, 100, 114, 128, 146, 164, 187, 210, 239, 269, 306, 345, 392, 443, 502, 568, 644, 729, 826, 935, 1059, 1199, 1358, 1538, 1742, 1973, 2235, 2531, 2867
Offset: 0

Views

Author

Bruno Berselli, Apr 24 2012

Keywords

Comments

a(n)/a(n-1) tends to (1+sqrt(65))/8 = 1.132782218537318706...

Crossrefs

Programs

  • Haskell
    a182280 n = a182280_list !! n
    a182280_list = 3 : 4 : zipWith (+)
                           a182280_list (map (flip div 4) $ tail a182280_list)
    -- Reinhard Zumkeller, Apr 30 2015
  • Magma
    [n le 2 select n+2 else Floor(Self(n-1)/4)+Self(n-2): n in [1..59]];
    
  • Mathematica
    RecurrenceTable[{a[0] == 3, a[1] == 4, a[n] == Floor(a[n - 1]/4) + a[n - 2]}, a, {n, 58}]
Showing 1-3 of 3 results.