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%I #14 Dec 06 2019 21:42:31
%S 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,2,2,1,
%T 1,1,1,1,1,2,3,2,1,1,1,1,1,1,2,3,3,2,1,1,1,1,1,1,2,3,4,3,2,1,1,1
%N A triangular central symmetric sequence based on the sequence A003269: if m <= floor(n/2), t(n,m) = A003269(m+2), otherwise t(n,m) = A003269(n - (m+2)).
%C Row sums: {1, 2, 3, 4, 5, 6, 8, 10, 13, 16, 20, ...}. [Is this A186445 or A080078? - _N. J. A. Sloane_, Feb 10 2013]
%C The A003269 sequence is pushed back twice, so that the triangle is not almost all ones.
%F a(n) = a(n-1) + a(n-4); t(n,m) = a(m) if m <= floor(n/2), a(n-m) otherwise.
%e {1},
%e {1, 1},
%e {1, 1, 1},
%e {1, 1, 1, 1},
%e {1, 1, 1, 1, 1},
%e {1, 1, 1, 1, 1, 1},
%e {1, 1, 1, 2, 1, 1, 1},
%e {1, 1, 1, 2, 2, 1, 1, 1},
%e {1, 1, 1, 2, 3, 2, 1, 1, 1},
%e {1, 1, 1, 2, 3, 3, 2, 1, 1, 1},
%e {1, 1, 1, 2, 3, 4, 3, 2, 1, 1, 1}
%t Clear[a]; a[ -2] = 0; a[ -1] = 1; a[0] = 1; a[1] = 1; a[n_] := a[n] = a[n - 1] + a[n - 4]; (* A003269 *) Table[If[m <= Floor[n/2],a[m],a[n-m] ] ,{n,0,10},{m,0,n}]
%Y Cf. A139147, A003269.
%K nonn,tabl,uned
%O 1,25
%A _Roger L. Bagula_ and _Gary W. Adamson_, May 31 2008
%E Non-ASCII characters removed and Mathematica code corrected by _Wouter Meeussen_, Feb 10 2013
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