A257273 a(n) = 2^(n-1)*(2^n+3).

2, 5, 14, 44, 152, 560, 2144, 8384, 33152, 131840, 525824, 2100224, 8394752, 33566720, 134242304, 536920064, 2147581952, 8590131200, 34360131584, 137439739904, 549757386752, 2199026401280, 8796099313664, 35184384671744, 140737513521152, 562950003752960, 2251799914348544, 9007199456067584

Offset: 0

Author

M. F. Hasler, Apr 27 2015

Keywords

• nonn
• easy

Comments

a(n) is in A125246 <=> n is in A057732 <=> A062709(n) is in A057733.

These are also the row sum of the triangle A146769: For n>=1, a(n-1) is the sum of row n of A146769.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-8).

Crossrefs

Cf. A000079, A007582, A028403, A256873, A256871, A257272.

Cf. A062709, A057732, A057733.

Programs

Magma

[2^(n-1)*(2^n+3): n in [0..35]]; // Vincenzo Librandi, Apr 27 2015

Mathematica

Table[2^(n - 1) (2^n + 3), {n, 0, 30}] (* Bruno Berselli, Apr 27 2015 *)
CoefficientList[Series[(2 - 7 x)/((1 - 4 x) (1 - 2 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Apr 27 2015 *)
LinearRecurrence[{6,-8},{2,5},30] (* Harvey P. Dale, Dec 21 2024 *)

PARI

a(n)=2^(n-1)*(2^n+3)

PARI

Vec((2-7*x)/((1-4*x)*(1-2*x)) + O(x^100)) \\ Colin Barker, Apr 27 2015

Formula

G.f.: (2-7*x)/((1-4*x)*(1-2*x)). - Vincenzo Librandi, Apr 27 2015

a(n) = 6*a(n-1)-8*a(n-2). - Colin Barker, Apr 27 2015