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 A073709 First differences of A073708. 7
 1, 1, 3, 3, 10, 10, 22, 22, 57, 57, 115, 115, 248, 248, 456, 456, 906, 906, 1598, 1598, 2956, 2956, 4980, 4980, 8802, 8802, 14422, 14422, 24440, 24440, 38856, 38856, 63881, 63881, 99515, 99515, 159106, 159106, 242654, 242654, 379609, 379609 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The convolution of this sequence results in A073710 and is equal to the first differences of the unique terms of this sequence. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 FORMULA G.f. satisfies: A(x) = A(x^2)^2/(1-x). G.f.: Product_{n>=0} 1/(1-x^(2^n))^(2^n). [Paul D. Hanna, May 01 2010] EXAMPLE G.f.: A(x) = 1 + x + 3*x^2 + 3*x^3 + 10*x^4 + 10*x^5 + 22*x^6 + 22*x^7 +... where A(x) =  A(x^2)^2/(1-x) and thus A(x) = 1 / [(1-x)*(1-x^2)^2*(1-x^4)^4*(1-x^8)^8*(1-x^16)^16*...]. Compare A(x)*(1-x) to A(x)^2: A(x)*(1-x) = 1 + 2*x^2 + 7*x^4 + 12*x^6 + 35*x^8 + 58*x^10 + 133*x^12 +... A(x)^2 = 1 + 2*x + 7*x^2 + 12*x^3 + 35*x^4 + 58*x^5 + 133*x^6 + 208*x^7 +... Also note that A(x)^2/(1-x) = 1 + 3*x + 10*x^2 + 22*x^3 + 57*x^4 + 115*x^5 + 248*x^6 + 456*x^7 +... MATHEMATICA terms = 42; For[m = 1; A = 1, m <= 2*terms, m = 2*m, A = ((1+x)*(Normal[A] /. x -> x^2))^2 + O[x]^m]; Join[{1}, Differences[CoefficientList[A, x] ]][[1 ;; terms]] (* Jean-François Alcover, Mar 06 2013, updated Apr 23 2016 *) PROG (PARI) {a(n)=polcoeff(prod(j=0, #binary(n), 1/(1-x^(2^j)+x*O(x^n))^(2^j)), n)} \\ Paul D. Hanna, May 01 2010 (Haskell) a073709 n = a073709_list !! n a073709_list = 1 : zipWith (-) (tail a073708_list) a073708_list --- Reinhard Zumkeller, Jun 13 2013 CROSSREFS Cf. A073707, A073708, A073710. Sequence in context: A278832 A168376 A266221 * A085288 A124630 A321397 Adjacent sequences:  A073706 A073707 A073708 * A073710 A073711 A073712 KEYWORD easy,nice,nonn AUTHOR Paul D. Hanna, Aug 05 2002 STATUS approved

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Last modified August 21 06:54 EDT 2019. Contains 326162 sequences. (Running on oeis4.)