0,3

Provides loss function for folding paper in half. It tells how much normalized paper has been lost with n folds. The sequence sets a limit on the number of times things of finite thickness can be folded in one direction.

Developed with J. R. Gallivan.

Binomial transform of A007051, with leading zero.

Second binomial transform of A078008(n-1)+0^n/2. - Paul Barry (pbarry(AT)wit.ie), Apr 27 2004

Britney C. Gallivan, How to fold paper in half twelve times (an "impossible challenge" solved and explained), Historical Society of Pomona Valley, Pomona California, (2002)

Eric Weisstein's World of Mathematics, Folding

a(n) = Sum_{k <= n} A007582(k).

G.f.: x(1-3x)/((1-x)(1-2x)(1-4x)); E.g.f.: exp(2x)/2+exp(4x)/6-2exp(x)/3; E.g.f.: exp(2x)(2cosh(x)/3-sinh(x)/3)-2/3; a(n)=sum{k=0..n, C(n, k)(3^(k-1)+1-4*0^k/3)/2}; a(n)=sum{k=0..n, C(n, k+1)(3^k+1)}.

a(12) = 2798250 means that for the 12th folding of paper in half that 2798250 times as much material has been lost to potential folding as was lost on the first fold.

(PARI) th(n)=if(n<1, y, th(n-1)*(th(n-1)+1)/2) and for(n=2, 30, print1(numerator(polcoeff(th(n), 2^n-3))", "))

Cf. A007582.

Sequence in context: A055990 A087945 A051924 this_sequence A062807 A117421 A034743

Adjacent sequences: A076021 A076022 A076023 this_sequence A076025 A076026 A076027

easy,nonn

Britney C. Gallivan (ogallivan(AT)verizon.net), Sep 30 2002

Example corrected by Rick L. Shepherd (rshepherd2(AT)hotmail.com), May 08 2003