A198645 -id:A198645 - cp's OEIS frontend

A155155 a(n) = 2(103^n - 1).

18, 58, 178, 538, 1618, 4858, 14578, 43738, 131218, 393658, 1180978, 3542938, 10628818, 31886458, 95659378, 286978138, 860934418, 2582803258, 7748409778, 23245229338, 69735688018, 209207064058, 627621192178, 1882863576538

Offset: 0

Paul Curtz, Jan 21 2009

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-3).

Cf. A003462, A048473.

[2*(10*3^n-1): n in [0..30]]; // Vincenzo Librandi, Aug 07 2011

seq(2*(10*3^n -1), n=0..30); # G. C. Greubel, Mar 20 2021

2*(10*3^Range[0,30] -1) (* G. C. Greubel, Mar 20 2021 *)

[2*(10*3^n - 1) for n in (0..30)] # G. C. Greubel, Mar 20 2021

a(n) = 4*a(n-1) - 3*a(n-2).
G.f.: ( 18 - 14*x ) / ( (1-x)*(1-3*x) ).
a(n) = 10*A048473(n) + 8 = A048473(n) + A048473(n+2).
a(n) = 3*a(n-1) - a(n-2) + 3*a(n-3) + 8.
From G. C. Greubel, Mar 20 2021: (Start)
a(n) = 18*A003462(n+1) - 14*A003462(n).
E.g.f.: 2*( 10*exp(3*x) - exp(x) ). (End)
a(n) = 2 * A198645(n). - Joerg Arndt, Mar 21 2021

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

Philippe Deléham, Feb 20 2014

Permutation of nonnegative integers.

			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, ...
...

Cf. A024023, A027107, A032766, A048473, A171498, A198643, A198644, A198645, A198646.

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).

cp's OEIS Frontend

A155155 a(n) = 2(103^n - 1).

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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.

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cp's OEIS Frontend

A155155 a(n) = 2*(10*3^n - 1).

Views

Author

Keywords

Links

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Programs

Magma

Maple

Mathematica

Sage

Formula

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.

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Author

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Comments

Examples

Crossrefs

Formula

A155155 a(n) = 2(103^n - 1).