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A214256
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Number of compositions of n where differences between neighboring parts are in {-2,-1,1,2}.
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2
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1, 1, 1, 3, 4, 5, 11, 14, 18, 36, 49, 66, 118, 169, 238, 401, 586, 846, 1371, 2042, 2998, 4731, 7114, 10566, 16419, 24809, 37118, 57139, 86558, 130151, 199193, 302109, 455737, 695084, 1054761, 1594484, 2426813, 3683310, 5575665, 8475607, 12864385, 19490762
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) ~ c * d^n, where d = 1.517398641547133636808941933115508174163721854365273284016518..., c = 0.733002948674062952076493110095119568735789170592785923762247... . - Vaclav Kotesovec, Sep 02 2014
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EXAMPLE
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a(4) = 4: [4], [3,1], [1,3], [1,2,1].
a(5) = 5: [5], [3,2], [2,3], [2,1,2], [1,3,1].
a(6) = 11: [6], [4,2], [3,2,1], [3,1,2], [2,4], [2,3,1], [2,1,3], [2,1,2,1], [1,3,2], [1,2,3], [1,2,1,2].
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MAPLE
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b:= proc(n, i) option remember; `if`(n<1 or i<1, 0,
`if`(n=i, 1, add(b(n-i, i+j), j=[-2, -1, 1, 2])))
end:
a:= n-> `if`(n=0, 1, add(b(n, j), j=1..n)):
seq(a(n), n=0..70);
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MATHEMATICA
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b[n_, i_] := b[n, i] = If[n < 1 || i < 1, 0, If[n == i, 1, Sum[b[n-i, i+j], {j, {-2, -1, 1, 2}}]]]; a[n_] := If[n == 0, 1, Sum[b[n, j], {j, 1, n}]]; Table[a[n], {n, 0, 70}] (* Jean-François Alcover, Nov 06 2014, after Alois P. Heinz *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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