A082384 a(0)=1, a(n)=2^n+n^2-2*a(n-1).

1, 6, 5, 22, 13, 74, 29, 262, 69, 986, 197, 3846, 669, 15242, 2509, 60774, 9813, 242842, 38965, 971046, 155501, 3883786, 621565, 15534662, 2485733, 62138074, 9942309, 248551622, 39768509, 994205706, 159073197, 3976821926, 636291829

Offset

0,2

Links

Table of n, a(n) for n=0..32.

Index entries for linear recurrences with constant coefficients, signature (3,1,-11,12,-4).

Formula

a(2n)=(1/27)*(25*4^n+36*n^2+24*n+2); a(2n+1)=(1/27)*(4*4^n+36*n^2+60*n+23)

a(0)=1, a(1)=1, a(2)=6, a(3)=5, a(4)=22, a(n)=3*a(n-1)+a(n-2)- 11*a(n-3)+ 12*a(n-4)-4*a(n-5) [From Harvey P. Dale, Apr 25 2012]

G.f.: -(4*x^4-12*x^3+14*x^2-3*x-1) / ((x-1)^3*(2*x-1)*(2*x+1)). [Colin Barker, Jun 26 2013]

Mathematica

RecurrenceTable[{a[0]==1, a[n]==2^n+n^2-2a[n-1]}, a, {n, 40}] (* or *) LinearRecurrence[{3, 1, -11, 12, -4}, {1, 1, 6, 5, 22}, 40] (* Harvey P. Dale, Apr 25 2012 *)

Prog

(PARI) a(n)=if(n<1, 1, 2^n+n^2-2*a(n-1))

Crossrefs

Sequence in context: A281221 A143130 A318547 * A248265 A267284 A228969

Adjacent sequences: A082381 A082382 A082383 * A082385 A082386 A082387

Keyword

nonn,easy

Author

Benoit Cloitre, Apr 13 2003

Status

approved