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

0,2

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

Table of n, a(n) for n=0..28.

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

Sequence in context: A026745 A139333 A099444 * A137166 A101890 A307573

Adjacent sequences: A132399 A132400 A132401 * A132403 A132404 A132405

Keyword

nonn,easy

Author

Paul Curtz, Nov 12 2007

Extensions

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

Status

approved