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A132402
Binomial transform of A004524 starting at 1.
0
1, 3, 7, 15, 32, 70, 156, 348, 768, 1672, 3600, 7696, 16384, 34784, 73664, 155584, 327680, 688256, 1442048, 3014912, 6291456, 13106688, 27261952, 56622080, 117440512, 243271680, 503320576, 1040191488, 2147483648
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.
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
Sequence in context: A139333 A099444 A374678 * A137166 A101890 A307573
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Nov 12 2007
EXTENSIONS
More terms from R. J. Mathar, Apr 02 2008
STATUS
approved