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 1-7 of 7 results.

A020065 Integer part of Gamma(n+7/9)/Gamma(7/9).

Original entry on oeis.org

1, 0, 1, 3, 14, 69, 400, 2714, 21115, 185345, 1812263, 19532170, 230045568, 2939471157, 40499380396, 598490843642, 9442855533026, 158430131720783, 2816535675036146, 52888281009012092, 1046012668844905826
Offset: 0

Views

Author

Simon Plouffe

Keywords

Links

Crossrefs

Cf. A020064, A020066, A020067, A020068, A020069.
Cf. A020020, A020110.

Programs

  • Magma
    [Truncate(Gamma(n+7/9)/Gamma(7/9)): n in [0..20]]; // G. C. Greubel, Nov 13 2019
  • Maple
    Digits := 64:f := proc(n,x) trunc(GAMMA(n+x)/GAMMA(x)); end;
seq(trunc(pochhammer(7/9,n)), n = 0..20); # G. C. Greubel, Nov 13 2019
  • Mathematica
    IntegerPart[Pochhammer[7/9, Range[0, 20]]] (* G. C. Greubel, Nov 13 2019 *)
  • PARI
    P(n,x) = gamma(x+n)/gamma(x);
vector(21, n, truncate(P(n-1, 7/9)) ) \\ G. C. Greubel, Nov 13 2019
  • Sage
    [int(rising_factorial(7/9, n)) for n in (0..20)] # G. C. Greubel, Nov 13 2019

A020066 Integer part of Gamma(n+5/9)/Gamma(5/9).

Original entry on oeis.org

1, 0, 0, 2, 7, 35, 198, 1302, 9843, 84216, 804738, 8494460, 98158213, 1232430908, 16706285646, 243169268856, 3782633071103, 62623591954942, 1099391947653437, 20399828362013787, 398929976857158503
Offset: 0

Views

Author

Simon Plouffe

Keywords

Links

Crossrefs

Cf. A020064, A020065, A020067, A020068, A020069.
Cf. A020021, A020111.

Programs

  • Magma
    [Truncate(Gamma(n+5/9)/Gamma(5/9)): n in [0..20]]; // G. C. Greubel, Nov 13 2019
  • Maple
    Digits := 64:f := proc(n,x) trunc(GAMMA(n+x)/GAMMA(x)); end;
seq(trunc(pochhammer(5/9,n)), n = 0..20); # G. C. Greubel, Nov 13 2019
  • Mathematica
    IntegerPart[Pochhammer[5/9, Range[0, 20]]] (* G. C. Greubel, Nov 13 2019 *)
  • PARI
    P(n,x) = gamma(x+n)/gamma(x);
vector(21, n, truncate(P(n-1, 5/9)) ) \\ G. C. Greubel, Nov 13 2019
  • Sage
    [int(rising_factorial(5/9, n)) for n in (0..20)] # G. C. Greubel, Nov 13 2019

A020067 Integer part of Gamma(n+4/9)/Gamma(4/9).

Original entry on oeis.org

1, 0, 0, 1, 5, 24, 130, 842, 6274, 52988, 500442, 5226841, 59818300, 744405515, 10008118594, 144561713037, 2232675345794, 36715105686390, 640474621418148, 11813198572823622, 229701083360459334, 4696111037591613052
Offset: 0

Views

Author

Simon Plouffe

Keywords

Links

Crossrefs

Cf. A020064, A020065, A020066, A020068, A020069.
Cf. A020022, A020112.

Programs

  • Magma
    [Truncate(Gamma(n+4/9)/Gamma(4/9)): n in [0..25]]; // G. C. Greubel, Nov 13 2019
  • Maple
    Digits := 64:f := proc(n,x) trunc(GAMMA(n+x)/GAMMA(x)) end: seq(f(n,4/9), n=0..25);
# alternative:
seq(trunc(pochhammer(4/9,n)), n = 0..25); # G. C. Greubel, Nov 13 2019
  • Mathematica
    IntegerPart[Pochhammer[4/9, Range[0, 25]]] (* G. C. Greubel, Nov 13 2019 *)
  • PARI
    P(n,x) = gamma(x+n)/gamma(x);
vector(26, n, truncate(P(n-1, 4/9)) ) \\ G. C. Greubel, Nov 13 2019
  • Sage
    [int(rising_factorial(4/9, n)) for n in (0..25)] # G. C. Greubel, Nov 13 2019

A020068 a(n) = floor( Gamma(n+2/9) / Gamma(2/9) ).

Original entry on oeis.org

1, 0, 0, 0, 1, 8, 42, 266, 1927, 15844, 146122, 1493700, 16762639, 204876708, 2708925368, 38526938568, 586465620430, 9513775620309, 163848357905335, 2985681188497227, 57391427290002261, 1160582196308934615
Offset: 0

Views

Author

Simon Plouffe

Keywords

Links

Crossrefs

Cf. A020064, A020065, A020066, A020067, A020069.
Cf. A020023, A020113.

Programs

  • Magma
    [Floor(Gamma(n+2/9)/Gamma(2/9)): n in [0..25]]; // G. C. Greubel, Nov 13 2019
  • Maple
    Digits := 64:f := proc(n,x) trunc(GAMMA(n+x)/GAMMA(x)); end;
seq(floor(pochhammer(2/9,n)), n = 0..25); # G. C. Greubel, Nov 13 2019
  • Mathematica
    Floor[Pochhammer[2/9, Range[0, 25]]] (* G. C. Greubel, Nov 13 2019 *)
  • PARI
    x=2/9; vector(26, n, gamma(n-1+x)\gamma(x) ) \\ G. C. Greubel, Nov 13 2019
  • Sage
    [floor(rising_factorial(2/9, n)) for n in (0..25)] # G. C. Greubel, Nov 13 2019

A020069 Integer part of Gamma(n+1/9)/Gamma(1/9).

Original entry on oeis.org

1, 0, 0, 0, 0, 3, 17, 104, 740, 6005, 54717, 553253, 6147263, 74450193, 976124760, 13774204958, 208143541601, 3353423725801, 57380805974819, 1039230152655057, 19860842917407765, 399423618672311729
Offset: 0

Views

Author

Simon Plouffe

Keywords

Links

Crossrefs

Cf. A020064, A020065, A020066, A020067, A020068.
Cf. A020024, A020114.

Programs

  • Magma
    [Truncate(Gamma(n+1/9)/Gamma(1/9)): n in [0..25]]; // G. C. Greubel, Nov 13 2019
  • Maple
    Digits := 64:f := proc(n,x) trunc(GAMMA(n+x)/GAMMA(x)); end;
seq(trunc(pochhammer(1/9,n)), n = 0..25); # G. C. Greubel, Nov 13 2019
  • Mathematica
    IntegerPart[Pochhammer[1/9, Range[0, 25]]] (* G. C. Greubel, Nov 13 2019 *)
  • PARI
    P(n,x) = gamma(x+n)/gamma(x);
vector(26, n, truncate(P(n-1, 1/9)) ) \\ G. C. Greubel, Nov 13 2019
  • Sage
    [int(rising_factorial(1/9, n)) for n in (0..25)] # G. C. Greubel, Nov 13 2019

A020019 Nearest integer to Gamma(n + 8/9)/Gamma(8/9).

Original entry on oeis.org

1, 1, 2, 5, 19, 92, 543, 3741, 29513, 262341, 2594262, 28248627, 335844793, 4328666215, 60120364101, 895125421053, 14222548356739, 240203038913808, 4296965473902563, 81164903395937306, 1614279745319197539, 33720510235556570814
Offset: 0

Views

Author

Simon Plouffe

Keywords

Comments

Gamma(n + 8/9)/Gamma(8/9) = 1, 8/9, 136/81, 3536/729, 123760/6561, 5445440/59049, 288608320/531441, 17893715840/4782969, ...

Links

Crossrefs

Cf. A049211, A020064, A020109.

Programs

  • Magma
    [Round(Gamma(n +8/9)/Gamma(8/9)): n in [0..30]]; // G. C. Greubel, Feb 03 2018
  • Maple
    Digits := 64:f := proc(n,x) round(GAMMA(n+x)/GAMMA(x)); end;
  • Mathematica
    f[n_] := Round[Gamma[n + 8/9]/Gamma[8/9]]; Array[f, 22, 0] (* Robert G. Wilson v, Sep 13 2013 *)
  • PARI
    for(n=0,30, print1(round(gamma(n+8/9)/gamma(8/9)), ", ")) \\ G. C. Greubel, Feb 03 2018

A182831 Joint-rank array of numbers j*r^(i-1), where r=1+sqrt(2), read by antidiagonals.

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 5, 11, 17, 22, 7, 14, 28, 45, 55, 9, 19, 37, 70, 112, 137, 10, 23, 48, 93, 171, 276, 334, 12, 26, 57, 118, 228, 417, 671, 812, 13, 31, 66, 141, 287, 556, 1010, 1627, 1965, 15, 34, 77, 164, 344, 697, 1347, 2444, 3934, 4751, 16, 39
Offset: 1

Views

Author

Clark Kimberling, Dec 07 2010

Keywords

Comments

Joint-rank arrays are defined in the first comment at A182801. (row 1)=A087063. First 3 columns are A020062, A020063, A020064.
Every positive integer occurs exactly once, so that as a sequence, this is a permutation of the positive integers.

Examples

			Northwest corner:
   1  2  4  5 ...
   3  6 11 14 ...
   8 17 28 37 ...
  22 45 70 93 ...
  ...

Links

Crossrefs

Cf. A182801.

Programs

  • Mathematica
    T[n_, k_] := Sum[Floor[k*(1 + Sqrt[2])^(n - j)], {j, 1, 100}]; Table[T[k + 1, n - k], {n,1,10}, {k, 0, n-1}]//Flatten (* G. C. Greubel, Aug 18 2018 *)

Formula

T(i,j) = Sum_{n>=1} floor(j*(1+sqrt(2))^(i-n)).
Showing 1-7 of 7 results.

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

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