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A091948 Number of values of k, 0 <= k <= n, satisfying A002487(k) = A002487(n).

%I A091948 #22 May 21 2024 08:46:12
%S A091948 1,1,2,1,3,1,2,2,4,1,3,1,3,2,4,2,5,3,3,1,5,1,4,2,4,3,5,2,6,4,4,6,6,1,
%T A091948 7,1,5,1,5,1,7,2,3,1,8,1,6,2,5,3,7,2,9,2,4,3,8,2,8,4,6,4,10,2,7,9,3,5,
%U A091948 11,1,5,3,7,1,6,1,10,1,3,4,9,2,7,1,5,1,5,2,12,2,3,2,11,1,6,8,6,9,7,2,12,3,4
%N A091948 Number of values of k, 0 <= k <= n, satisfying A002487(k) = A002487(n).
%C A091948 This sequence is the ordinal transform of A002487. - _Rémy Sigrist_, Dec 28 2022
%H A091948 Rémy Sigrist, <a href="/A091948/b091948.txt">Table of n, a(n) for n = 0..8192</a>
%H A091948 Rémy Sigrist, <a href="/A091948/a091948.gp.txt">PARI program</a>
%H A091948 <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>
%F A091948 a(n) = 1 iff n belongs to A091945. - _Rémy Sigrist_, Dec 28 2022
%p A091948 b:= proc(n) option remember; `if`(n<2, n,
%p A091948       (q-> b(q)+(n-2*q)*b(n-q))(iquo(n, 2)))
%p A091948     end:
%p A091948 p:= proc() 0 end:
%p A091948 a:= proc(n) option remember; local t;
%p A091948       t:= b(n); p(t):= p(t)+1
%p A091948     end:
%p A091948 seq(a(n), n=0..100);  # _Alois P. Heinz_, Dec 31 2022
%t A091948 b[n_] := b[n] = If[n < 2, n,
%t A091948    Function[q, b[q] + (n - 2*q)*b[n - q]][Quotient[n, 2]]];
%t A091948 p[_] = 0;
%t A091948 a[n_] := a[n] = With[{t = b[n]}, p[t] = p[t]+1];
%t A091948 Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, May 20 2024, after _Alois P. Heinz_ *)
%o A091948 (PARI) \\ See Links section.
%Y A091948 Cf. A002487, A091945.
%K A091948 nonn,look
%O A091948 0,3
%A A091948 _Benoit Cloitre_, Mar 11 2004
%E A091948 a(0) = 1 prepended and name adapted by _Rémy Sigrist_, Dec 28 2022