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 1-4 of 4 results.

A198643 a(n) = 5*3^n-1.

Original entry on oeis.org

4, 14, 44, 134, 404, 1214, 3644, 10934, 32804, 98414, 295244, 885734, 2657204, 7971614, 23914844, 71744534, 215233604, 645700814, 1937102444, 5811307334, 17433922004, 52301766014, 156905298044, 470715894134, 1412147682404, 4236443047214
Offset: 0

Views

Author

Vincenzo Librandi, Oct 28 2011

Keywords

Crossrefs

Programs

  • Magma
    [5*3^n-1: n in [0..30]];
    
  • Mathematica
    5*3^Range[0, 30] - 1 (* or *)
    NestList[3*# + 2 &, 4, 30] (* Paolo Xausa, Aug 28 2024 *)
  • PARI
    a(n)=5*3^n-1 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = 3*a(n-1)+2 = 2*A060816(n+1).
G.f.: ( 4-2*x ) / ( (3*x-1)*(x-1) ). - R. J. Mathar, Nov 17 2011

A182950 Joint-rank array of the numbers (3*i+2)*3^j, where i>=0, j>=0, by antidiagonals.

Original entry on oeis.org

1, 3, 2, 9, 7, 4, 27, 22, 12, 5, 81, 67, 36, 16, 6, 243, 202, 108, 49, 20, 8, 729, 607, 324, 148, 62, 25, 10, 2187, 1822, 972, 445, 188, 76, 30, 11, 6561, 5467, 2916, 1336, 566, 229, 90, 34, 13, 19683, 16402, 8748, 4009, 1700, 688, 270, 103, 39, 14
Offset: 1

Views

Author

Clark Kimberling, Dec 15 2010

Keywords

Comments

Joint-rank arrays are defined in the first comment at A182801. As for any joint-rank array, A182950 is a permutation of the positive integers, but, a fortiori, A182950 is an interspersion: after initial terms every row is interspersed with all other rows. The numbers (3*i+2)*3^j as an array comprise A182830; and sorted, possibly A026179.
(row 1)=A000244.
(row 2)=A060816.
(row 3)=A003946.
(row 4)=A052909.
(row 5)=A027107?

Examples

			Northwest corner:
1....3....9....27...
2....7...22....67...
4...12...36...108...
5...16...49...148...
		

Crossrefs

Programs

  • Mathematica
     M[i_,j_]:=j+Floor[Log[3*i/2+1]/Log[3]];
     T[i_,j_]:=Sum[Floor[1/3+(3*i+2)*3^(j-k-1)],{k,0,M[i,j]}];
     TableForm[Table[T[i,j],{i,0,9},{j,0,9}]]

A198646 a(n) = 11*3^n-1.

Original entry on oeis.org

10, 32, 98, 296, 890, 2672, 8018, 24056, 72170, 216512, 649538, 1948616, 5845850, 17537552, 52612658, 157837976, 473513930, 1420541792, 4261625378, 12784876136, 38354628410, 115063885232, 345191655698, 1035574967096, 3106724901290
Offset: 0

Views

Author

Vincenzo Librandi, Oct 28 2011

Keywords

Crossrefs

Programs

  • Magma
    [11*3^n-1: n in [0..30]]
  • Mathematica
    11*3^Range[0, 30] - 1 (* Wesley Ivan Hurt, Oct 02 2021 *)

Formula

a(n) = 3*a(n-1)+2, a(0)=10.
G.f.: (10-8*x) / ((3*x-1)*(x-1)). - R. J. Mathar, Oct 30 2011
a(n) = 4*a(n-1)-3*a(n-2). - Wesley Ivan Hurt, Oct 02 2021
a(n) = 2*A052909(n+1). - R. J. Mathar, Apr 07 2022

A238207 Square array T(n,k), n>=0, k>=0, read by antidiagonals, where T(0,k) is A032766(k) and T(n,k) = 3*T(n-1,k) + 2 for n>0.

Original entry on oeis.org

0, 1, 2, 3, 5, 8, 4, 11, 17, 26, 6, 14, 35, 53, 80, 7, 20, 44, 107, 161, 242, 9, 23, 62, 134, 323, 485, 728, 10, 29, 71, 188, 404, 971, 1457, 2186, 12, 32, 89, 215, 566, 1214, 2915, 4373, 6560, 13, 28, 98, 269, 647, 1700, 3644, 8747, 13121, 19682, 15, 41, 116
Offset: 0

Views

Author

Philippe Deléham, Feb 20 2014

Keywords

Comments

Permutation of nonnegative integers.

Examples

			Square array begins:
0, 1, 3, 4, 6, 7, 9, 10, ...
2, 5, 11, 14, 20, 23, 29, 32, ...
8, 17, 35, 44, 62, 71, 89, 98, ...
26, 53, 107, 134, 188, 215, 269, 296, ...
80, 161, 323, 404, 566, 647, 809, 890, ...
242, 485, 971, 1214, 1700, 1943, 2429, 2672, ...
728, 1457, 2915, 3644, 5102, 5831, 7289, 8018, ...
2186, 4373, 8747, 10934, 15308, 17495, 21869, 24056, ...
...
		

Crossrefs

Formula

T(n,k) = T(0,k)*3^n + T(n,0) where T(0,k) = A032766(k) and T(n,0) = 3^n - 1 = A024023(n).
Showing 1-4 of 4 results.