A132402 Binomial transform of A004524 starting at 1.

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

Author

Paul Curtz, Nov 12 2007

Keywords

• nonn
• easy

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).

Programs

Mathematica

LinearRecurrence[{6,-14,16,-8},{1,3,7,15},30] (* Harvey P. Dale, Mar 30 2022 *)

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

Extensions

More terms from R. J. Mathar, Apr 02 2008