A172416 a(n) = 5*2^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

0,3

Comments

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.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,3,-1,-2).

Formula

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 ).

Prog

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

Crossrefs

Sequence in context: A224073 A034774 A342536 * A317883 A337089 A144958

Adjacent sequences: A172413 A172414 A172415 * A172417 A172418 A172419

Keyword

nonn,easy

Author

Paul Curtz, Feb 02 2010

Status

approved