

A212306


Starting with the positive numbers, each element subtracts its value, a(n), from the next a(n) elements.


3



1, 1, 2, 2, 1, 3, 4, 1, 1, 5, 2, 5, 1, 3, 2, 6, 1, 11, 2, 1, 1, 4, 8, 1, 1, 2, 6, 1, 3, 13, 1, 9, 5, 7, 1, 1, 2, 2, 6, 3, 3, 17, 1, 17, 5, 7, 1, 1, 2, 2, 6, 3, 3, 8, 1, 4, 5, 7, 1, 18, 6, 18, 14, 1, 1, 9, 2, 7, 1, 3, 2, 1, 1, 7, 2, 17, 1, 17, 20, 1, 19, 9, 1, 1
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OFFSET

1,3


COMMENTS

When calculating this sequence, each element affects a different number of subsequent terms, so there is no known direct formula for the nth term.
a(A258353(n)) = 1; a(A258354(n)) = n and a(m) != n for m < A258354(n).  Reinhard Zumkeller, May 27 2015


LINKS

Paul D. Hanna, Table of n, a(n) for n = 1..10000


FORMULA

a(n) is n  the sum of the terms such that a(i) + i >= n.
Each term a(n) is 1 plus the sum of the terms such that a(i) + i + 1 = n.


EXAMPLE

Starting with A000027, the first term is 1 so we subtract 1 from the next 1 terms so the second term becomes 1. Now again we subtract 1 from the next 1 terms and the third term becomes 2. Subtract 2 from the next two terms of A000027 (4 and 5) to get 2 and 3. Subtract 2 from the next 2 terms (the 3 from 5 and 6) to get 1 and 4. The next term is 4  1 = 3. To carry on subtract 3 from the next 3 terms.


MAPLE

b:= proc(n) option remember; local l, t;
if n=1 then [1$2] else l:= b(n1); t:= nl[2];
zip((x, y)>x+y, [t$t+1], subsop(1=NULL, 2=0, l), 0) fi
end:
a:= n> b(n)[1]:
seq(a(n), n=1..100); # Alois P. Heinz, Nov 12 2013


MATHEMATICA

b[n_] := b[n] = Module[{l, t, x, y, m}, If[n == 1, {1, 1}, l = b[n1]; t = nl[[2]]; x = Array[t&, t+1]; y = ReplacePart[l, {1 > Sequence[], 2 > 0}]; m = Max[Length[x], Length[y]]; Thread[PadRight[x, m] + PadRight[y, m]]]]; a[n_] := b[n] // First; Table[a[n], {n, 1, 100}] (* JeanFrançois Alcover, Jan 27 2014, after Alois P. Heinz *)


PROG

(PARI) {a(n)=local(A=vector(n+1, j, j)); for(k=1, n+1, A = Vec(Ser(A)  x^k*A[k]*(1x^A[k])/(1x) +x*O(x^n))); A[n]} \\ Paul D. Hanna, Nov 12 2013
for(n=1, 100, print1(a(n), ", "))
(PARI) /* Vector returns 1000 terms: */
{A=vector(1000, j, j); for(k=1, #A, A = Vec(Ser(A)  x^k*A[k]*(1x^A[k])/(1x) +x*O(x^#A))); A} \\ Paul D. Hanna, Nov 12 2013
(Haskell)
a212306 n = a212306_list !! (n1)
a212306_list = f [1..] where
f (x:xs) = x : f ((map (subtract x) us) ++ vs)
where (us, vs) = splitAt x xs
 Reinhard Zumkeller, Dec 16 2013


CROSSREFS

Generated from A000027.
Cf. A258353, A258354.
Sequence in context: A181512 A076019 A071453 * A339708 A080242 A183927
Adjacent sequences: A212303 A212304 A212305 * A212307 A212308 A212309


KEYWORD

nonn,nice


AUTHOR

Gabriel Stauth, Oct 26 2013


STATUS

approved



