OFFSET
0,2
COMMENTS
Twisted numbers. b(n)=a(n)-2^n=0, 1, 3, 7, 16, 38, 92, 220, 512, 1160, 2576, twisted numbers. b(n+1)-2b(n)=1, 1, 1, 2, 6, 16, 36, 72, 136, 256.
LINKS
Index entries for linear recurrences with constant coefficients, signature (6,-14,16,-8).
FORMULA
a(n+1)-2a(n) = 1, 1, 1, 2, 6, 16, 36, 72, 136, 256 = essentially A038503.
O.g.f.: (1-x)^3/[(1-2x+2x^2)(-1+2x)^2]. a(n)=6*a(n-1)-14*a(n-2)+16*a(n-3)-8*a(n-4). - R. J. Mathar, Apr 02 2008
4*a(n) = (n+4)*2^n+2*A009545(n). - R. J. Mathar, Nov 01 2021
MATHEMATICA
LinearRecurrence[{6, -14, 16, -8}, {1, 3, 7, 15}, 30] (* Harvey P. Dale, Mar 30 2022 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Nov 12 2007
EXTENSIONS
More terms from R. J. Mathar, Apr 02 2008
STATUS
approved