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 A224959 Number of compositions [p(1), p(2), ..., p(k)] of n such that p(j) - p(j-1) <= 2 4
 1, 1, 2, 4, 8, 15, 29, 55, 105, 199, 378, 716, 1358, 2572, 4873, 9229, 17480, 33102, 62688, 118709, 224795, 425676, 806068, 1526371, 2890338, 5473125, 10363871, 19624925, 37161558, 70368705, 133249369, 252319408, 477788980, 904735349, 1713195705, 3244086145 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..3607 FORMULA a(n) ~ c * d^n, where d=1.893587506319686491635881459546948770530553555112342985931092896452453511... and c=0.6398882559654423774981963082429746674258714212085034829366885993226... - Vaclav Kotesovec, May 01 2014 EXAMPLE There are a(5) = 15 such compositions of 5: 01:  [ 1 1 1 1 1 ] 02:  [ 1 1 1 2 ] 03:  [ 1 1 2 1 ] 04:  [ 1 1 3 ] 05:  [ 1 2 1 1 ] 06:  [ 1 2 2 ] 07:  [ 1 3 1 ] 08:  [ 2 1 1 1 ] 09:  [ 2 1 2 ] 10:  [ 2 2 1 ] 11:  [ 2 3 ] 12:  [ 3 1 1 ] 13:  [ 3 2 ] 14:  [ 4 1 ] 15:  [ 5 ] (the single forbidden composition is [ 1 4 ]). MAPLE b:= proc(n, i) option remember;       `if`(n=0, 1, add(b(n-j, max(1, j-2)), j=i..n))     end: a:= n-> b(n, 1): seq(a(n), n=0..40);  # Alois P. Heinz, May 02 2013 CROSSREFS Cf. A003116 (compositions such that p(j) - p(j-1) <= 1). Cf. A225084 (triangle: compositions of n such that max(p(j) - p(j-1)) = k). Cf. A225085 (triangle: compositions of n such that max(p(j) - p(j-1)) <= k). Sequence in context: A217733 A208976 A278554 * A108564 A066369 A239555 Adjacent sequences:  A224956 A224957 A224958 * A224960 A224961 A224962 KEYWORD nonn AUTHOR Joerg Arndt, Apr 21 2013 STATUS approved

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Last modified October 15 01:40 EDT 2019. Contains 328025 sequences. (Running on oeis4.)