This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A171238 #44 May 12 2024 16:19:20
%S A171238 1,2,5,8,16,24,40,56,88,120,176,232,328,424,576,728,968,1208,1568,
%T A171238 1928,2464,3000,3768,4536,5632,6728,8248,9768,11864,13960,16784,19608,
%U A171238 23400,27192,32192,37192,43760,50328,58824,67320,78280,89240,103200,117160
%N A171238 Given M = triangle A122196 as an infinite lower triangular matrix, this sequence is lim_{k->infinity} M^k.
%C A171238 Also equals polcoeff: (1,2,3,...)*(1,0,2,0,5,0,8,0,16,...).
%C A171238 Number of binary partitions of n into two kinds of parts. - _Joerg Arndt_, Feb 26 2015
%C A171238 Let the n-th convolution power of the sequence = B, with C = the aerated variant of B. It appears that B/C = the binomial sequence starting (1, 2n, ...). Example: The sequence squared = (1, 4, 14, 36, 89, 192, ...) = B; with C = (1, 0, 4, 0, 14, 0, 36, ...). Then B/C = A000292: (1, 4, 10, 20, 35, 56, ...). - _Gary W. Adamson_, Aug 15 2016
%H A171238 Georg Fischer, <a href="/A171238/b171238.txt">Table of n, a(n) for n = 1..1000</a> [first 128 terms from Vincenzo Librandi]
%F A171238 Given M = triangle A122196 as an infinite lower triangular matrix, this sequence is lim_{k->infinity}, a left-shifted vector considered as a sequence.
%F A171238 From _Wolfdieter Lang_, Jul 15 2010: (Start)
%F A171238 O.g.f.: x*Q(x) with Q(x)*(1-x)^2 = Q(x^2), for the eigensequence M*Q = Q with the column o.g.f.s (x^(2*m))/(1-x)^2, m >= 0, of M.
%F A171238 Recurrence for b(n):=a(n+1): b(n)=0 if n < 0, b(0)=1; if n is even then b(n) = b(n/2) + 2*b(n-1) - b(n-2), otherwise b(n) = 2*b(n-1) - b(n-2). (End)
%F A171238 G.f.: 1/((1-x)*(1-x^2)*(1-x^4)* ... *(1- x^(2^k))* ...)^2. - _Robert G. Wilson v_, May 11 2012
%F A171238 Convolution square of A018819. - _Michael Somos_, Mar 28 2014
%e A171238 G.f. = x + 2*x^2 + 5*x^3 + 8*x^4 + 16*x^5 + 24*x^6 + 40*x^7 + 56*x^8 + ...
%t A171238 imax=10; CoefficientList[ Series[ 1/ Product[1 - x^(2^i), {i, 0, imax}]^2, {x, 0, 2^imax}], x] (* _Robert G. Wilson v_, May 11 2012; range of "i" amended by _Georg Fischer_, May 12 2024 *)
%Y A171238 Cf. A000292, A018819, A122196.
%K A171238 nonn
%O A171238 1,2
%A A171238 _Gary W. Adamson_, Dec 05 2009
%E A171238 More terms from _Wolfdieter Lang_, Jul 15 2010