A180516 Numbers of the form i*4^j-1 (i=1..3, j >= 0).

0, 1, 2, 3, 7, 11, 15, 31, 47, 63, 127, 191, 255, 511, 767, 1023, 2047, 3071, 4095, 8191, 12287, 16383, 32767, 49151, 65535, 131071, 196607, 262143, 524287, 786431, 1048575, 2097151, 3145727, 4194303, 8388607, 12582911, 16777215, 33554431, 50331647, 67108863, 134217727, 201326591, 268435455, 536870911, 805306367, 1073741823, 2147483647, 3221225471

Offset: 1

Author

N. J. A. Sloane, Jan 25 2011

Keywords

• nonn
• easy

Links

• Paolo Xausa, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,4,-4).

Crossrefs

Smallest number whose base b sum of digits is n: A000225 (b=2), A062318 (b=3), this sequence (b=4), A181287 (b=5), A181288 (b=6), A181303 (b=7), A165804 (b=8), A140576 (b=9), A051885 (b=10). - Jason Kimberley, Nov 02 2011

Programs

Mathematica

LinearRecurrence[{1, 0, 4, -4}, Range[0, 3], 50] (* Paolo Xausa, Aug 27 2024 *)

Formula

From Colin Barker, Feb 01 2013: (Start)

a(n) = a(n-1) + 4*a(n-3) - 4*a(n-4).

G.f.: x^2*(x^2+x+1) / ((x-1)*(4*x^3-1)). (End)