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 A076024 (2^n+4)*(2^n-1)/6. 2
 0, 1, 4, 14, 50, 186, 714, 2794, 11050, 43946, 175274, 700074, 2798250, 11188906, 44747434, 178973354, 715860650, 2863377066, 11453377194, 45813246634, 183252462250, 733008800426, 2932033104554, 11728128223914, 46912504507050, 187650001250986, 750599971449514 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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, Apr 27 2004 REFERENCES 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) LINKS Ivan Panchenko, Table of n, a(n) for n = 0..200 Eric Weisstein's World of Mathematics, Folding Index entries for linear recurrences with constant coefficients, signature (7,-14,8). FORMULA a(n) = Sum_{k <= n} A007582(k). G.f.: x*(1-3*x)/((1-x)*(1-2*x)*(1-4*x)). E.g.f.: exp(2*x)/2+exp(4*x)/6-2*exp(x)/3 = exp(2*x)*(2*cosh(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(n) = Sum_{i < n} a(i) + A073724(n-1). - Ivan N. Ianakiev, Jun 12 2014 EXAMPLE 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. MAPLE A076024:=n->(2^n + 4)*(2^n - 1)/6; seq(A076024(n), n=0..30); # Wesley Ivan Hurt, Jun 12 2014 MATHEMATICA Table[(2^n + 4)*(2^n - 1)/6, {n, 0, 30}] (* Wesley Ivan Hurt, Jun 12 2014 *) PROG (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))", ")) (MAGMA) [ (2^n + 4)*(2^n - 1)/6 : n in [0..30] ]; // Wesley Ivan Hurt, Jun 12 2014 CROSSREFS Cf. A007582. Sequence in context: A087945 A051924 A272687 * A062807 A117421 A034743 Adjacent sequences:  A076021 A076022 A076023 * A076025 A076026 A076027 KEYWORD easy,nonn AUTHOR Britney C. Gallivan (ogallivan(AT)verizon.net), Sep 30 2002 EXTENSIONS Example corrected by Rick L. Shepherd, May 08 2003 STATUS approved

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Last modified December 18 18:07 EST 2018. Contains 318243 sequences. (Running on oeis4.)