A172447 -id:A172447 - cp's OEIS frontend

A172416 a(n) = 52^n/9 + 1/4 + (-1)^n(n/6 + 7/36).

1, 1, 3, 4, 10, 17, 37, 70, 144, 283, 571, 1136, 2278, 4549, 9105, 18202, 36412, 72815, 145639, 291268, 582546, 1165081, 2330173, 4660334, 9320680, 18641347, 37282707, 74565400, 149130814, 298261613, 596523241

Offset: 0

Paul Curtz, Feb 02 2010

The sequence and the 1st, 2nd, 3rd etc. difference form the array
1, 1, 3, 4, 10, 17, 37, 70, 144, 283, 571, 1136,..
0, 2, 1, 6, 7, 20, 33, 74, 139, 288, 565, 1142, 2271,..
2, -1, 5, 1, 13, 13, 41, 65, 149, 277, 577, 1129, 2285,..
-3, 6, -4, 12, 0, 28, 24, 84, 128, 300, 552, 1156,...
where the sequence 1,2,5,12,.... = A045623 appears on the diagonal.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,3,-1,-2).

[5*2^n/9 +1/4 +(-1)^n*(n/6+7/36): n in [0..40]]; // Vincenzo Librandi, Aug 05 2011

a(n) = a(n-1) + 3*a(n-2) - a(n-3) - 2*a(n-4).
a(n+1) - a(n) = A172285(n).
a(2n) = A164044(n).
a(2n+1) = A172447(n).
a(n+1) - 2*a(n) = (-1)^(n+1)*A008619(n).
G.f.: ( 1 - x^2 - x^3 ) / ( (2*x-1)*(x-1)*(1+x)^2 ).

cp's OEIS Frontend

A172416 a(n) = 52^n/9 + 1/4 + (-1)^n(n/6 + 7/36).

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cp's OEIS Frontend

A172416 a(n) = 5*2^n/9 + 1/4 + (-1)^n*(n/6 + 7/36).

Views

Author

Keywords

Comments

Links

Programs

Magma

Formula

A172416 a(n) = 52^n/9 + 1/4 + (-1)^n(n/6 + 7/36).