Search: id:A152537
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%I A152537
%S A152537 1,1,1,2,4,9,18,37,74,148,296,592,1183
%N A152537 Convolution sequence: convolved with A000041 = powers of 2, (A000079).
%F A152537 Construct an array of rows such that n-th row = partial sums of (n-1)-th 
               row
%F A152537 of A010815: (1, -1, -1, 0, 0, 1, 0, 1,...).
%F A152537 A152537 = sums of antidiagonal terms of the array.
%F A152537 The sequence may be obtained directly from the following set of operations:
%F A152537 Our given sequence = A000041: (1, 1, 2, 3, 5, 7, 11,...). Delete the 
               first
%F A152537 "1" then consider (1, 2, 3, 5, 7, 11,...) as an operator Q which we write 
               in reverse with 1,2,3,...terms for each operation. Letting R = the 
               target sequence (1,2,4,8,...); we begin a(0) = 1, a(1) = 1, then 
               perform successive
%F A152537 operations of: "next term in (1,2,4,...) - dot product of Q*R" where 
               Q is
%F A152537 written right to left and R (the ongoing result) written left to right).
%F A152537 Examples: Given 4 terms Q, R, we have: (5,3,2,1) dot (1,1,1,2) = (5+3+2+2) 
               =
%F A152537 12, which we subtract from 16, = 4.
%F A152537 Given 5 terms of Q,R and A152537, we have (7,5,3,2,1) dot (1,1,1,2,4) 
               = 23
%F A152537 which is subtracted from 32 giving 9. Continue with analogous operations 
               to generate the series.
%F A152537 a(n)=sum_{j=0..n} A010815(j)*2^(n-j). G.f.: A000079(x)/A000041(x) = A010815(x)/
               (1-2x), where A......(x) denotes the g.f. of the associated sequence. 
               [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 09 2008]
%e A152537 a(5) = 9 = 32 - 23 = (32 - ((7,5,3,2,1) dot (1,1,1,2,4)))
%e A152537 (1,1,2,3) convolved with (1,1,1,2) = 8, where (1,1,2,3...) = the first 
               four partition numbers.
%Y A152537 Cf. A010815, A000041, A000079, A152538
%Y A152537 Sequence in context: A033138 A155803 A056185 this_sequence A081253 A118255 
               A019299
%Y A152537 Adjacent sequences: A152534 A152535 A152536 this_sequence A152538 A152539 
               A152540
%K A152537 nonn
%O A152537 0,4
%A A152537 Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 06 2008

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