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 A048888 a(n) = Sum{T(m,n+1-m): m=1,2,...,n}, array T as in A048887. 16
 0, 1, 2, 4, 7, 13, 23, 42, 76, 139, 255, 471, 873, 1627, 3044, 5718, 10779, 20387, 38673, 73561, 140267, 268065, 513349, 984910, 1892874, 3643569, 7023561, 13557019, 26200181, 50691977, 98182665, 190353369, 369393465, 717457655 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS From Marc LeBrun, Dec 12 2001: (Start) Define a "numbral arithmetic" by replacing addition with binary bitwise inclusive-OR (so that [3] + [5] = [7] etc.) and multiplication becomes shift-&-OR instead of shift-&-add (so that [3] * [3] = [7] etc.). [d] divides [n] means there exists an [e] with [d] * [e] = [n]. For example the six divisors of [14] are [1], [2], [3], [6], [7] and [14]. Then it appears that this sequence gives the number of proper divisors of [2^n-1]. Conjecture confirmed by Richard C. Schroeppel, Dec 14 2001. (End) The number of "prime endofunctions" on n points, meaning the cardinality of the subset of the A001372(n) mappings (or mapping patterns) up to isomorphism from n (unlabeled) points to themselves (endofunctions) which are neither the sum of prime endofunctions (i.e., whose disjoint connected components are prime endofunctions) nor the categorical product of prime endofunctions. The n for which a(n) is prime (n such that the number of prime endofunctions on n points is itself prime) are 2, 4, 5, 6, 9, 13, 19, ... - Jonathan Vos Post, Nov 19 2006 For n>=1, compositions p(1)+p(2)+...+p(m)=n such that p(k)<=p(1)+1, see example. - Joerg Arndt, Dec 28 2012 LINKS D. Applegate, M. LeBrun, N. J. A. Sloane, Dismal Arithmetic, J. Int. Seq. 14 (2011) # 11.9.8. A. Frosini and S. Rinaldi, On the Sequence A079500 and Its Combinatorial Interpretations, J. Integer Seq., Vol. 9 (2006), Article 06.3.1. FORMULA G.f.: Sum_{k>0} x^k*(1-x^k)/(1-2*x+x^(k+1)). - Vladeta Jovovic, Feb 25 2003 a(m) = Sum_{ n=2..m+1 } Fn(m) where Fn is a Fibonacci n-step number (Fibonacci, tetranacci, etc.) indexed as in A000045, A000073, A000078. - Gerald McGarvey, Sep 25 2004 EXAMPLE From Joerg Arndt, Dec 28 2012: (Start) There are a(6)=23 compositions p(1)+p(2)+...+p(m)=6 such that p(k)<=p(1)+1: [ 1]  [ 1 1 1 1 1 1 ] [ 2]  [ 1 1 1 1 2 ] [ 3]  [ 1 1 1 2 1 ] [ 4]  [ 1 1 2 1 1 ] [ 5]  [ 1 1 2 2 ] [ 6]  [ 1 2 1 1 1 ] [ 7]  [ 1 2 1 2 ] [ 8]  [ 1 2 2 1 ] [ 9]  [ 2 1 1 1 1 ] [10]  [ 2 1 1 2 ] [11]  [ 2 1 2 1 ] [12]  [ 2 1 3 ] [13]  [ 2 2 1 1 ] [14]  [ 2 2 2 ] [15]  [ 2 3 1 ] [16]  [ 3 1 1 1 ] [17]  [ 3 1 2 ] [18]  [ 3 2 1 ] [19]  [ 3 3 ] [20]  [ 4 1 1 ] [21]  [ 4 2 ] [22]  [ 5 1 ] [23]  [ 6 ] (End) PROG (PARI) N = 66;  x = 'x + O('x^N); gf = sum(n=0, N,  (1-x^n)*x^n/(1-2*x+x^(n+1)) ) + 'c0; v = Vec(gf);  v[1]-='c0;  v /* Joerg Arndt, Apr 14 2013 */ CROSSREFS Cf. A007059. Cf. A000312, A001372, A002861, A006961, A001373, A054050, A054745, A125024. Sequence in context: A287381 A078038 A190502 * A280027 A026724 A054163 Adjacent sequences:  A048885 A048886 A048887 * A048889 A048890 A048891 KEYWORD nonn AUTHOR STATUS approved

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Last modified November 16 15:26 EST 2018. Contains 317274 sequences. (Running on oeis4.)