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 A157268 An additive three term general recursion with always even third term: Tent function(even):f(n,m)=If[k <= Floor[n/2], 2^k, 2^(n - k)]; Recursion: m=1; A(n,k,m)=(m*(n - k) + 1)*A(n - 1, k - 1, m) + (m*k + 1)*A(n - 1, k, m) + m*f[n, k]*A(n - 2, k - 1, m). 0

%I

%S 1,1,1,1,6,1,1,17,17,1,1,40,126,40,1,1,87,606,606,87,1,1,182,2413,

%T 5856,2413,182,1,1,373,8679,40337,40337,8679,373,1,1,756,29376,232726,

%U 497066,232726,29376,756,1,1,1523,95668,1205968,4527078,4527078,1205968,95668

%N An additive three term general recursion with always even third term: Tent function(even):f(n,m)=If[k <= Floor[n/2], 2^k, 2^(n - k)]; Recursion: m=1; A(n,k,m)=(m*(n - k) + 1)*A(n - 1, k - 1, m) + (m*k + 1)*A(n - 1, k, m) + m*f[n, k]*A(n - 2, k - 1, m).

%C Row sums are:

%C {1, 2, 8, 36, 208, 1388, 11048, 98780, 1022784, 11660476, 152094648,...}. With an ordinary tent function the third terms adds both even and odd values.

%C In this case the result is fixed on only adding even third term factors.

%F Tent function(even):f(n,m)=If[k <= Floor[n/2], 2^k, 2^(n - k)];

%F Recursion: m=1;

%F A(n,k,m)=(m*(n - k) + 1)*A(n - 1, k - 1, m) +

%F (m*k + 1)*A(n - 1, k, m) +

%F m*f[n, k]*A(n - 2, k - 1, m).

%e {1},

%e {1, 1},

%e {1, 6, 1},

%e {1, 17, 17, 1},

%e {1, 40, 126, 40, 1},

%e {1, 87, 606, 606, 87, 1},

%e {1, 182, 2413, 5856, 2413, 182, 1},

%e {1, 373, 8679, 40337, 40337, 8679, 373, 1},

%e {1, 756, 29376, 232726, 497066, 232726, 29376, 756, 1},

%e {1, 1523, 95668, 1205968, 4527078, 4527078, 1205968, 95668, 1523, 1},

%e {1, 3058, 303735, 5824224, 34800782, 70231048, 34800782, 5824224, 303735, 3058, 1}

%t Clear[A, f, n, k, m];

%t f[n_, k_] := If[k <= Floor[n/2], 2^k, 2^(n - k)];

%t A[n_, 0, m_] := 1; A[n_, n_, m_] := 1;

%t A[n_, k_, m_] := (m*(n - k) + 1)*A[n - 1, k - 1, m] + (m*k + 1)*A[n - 1, k, m] + m*f[n, k]*A[n - 2, k - 1, m];

%t Table[A[n, k, m], {m, 0, 10}, {n, 0, 10}, {k, 0, n}];

%t Table[Flatten[Table[Table[A[n, k, m], {k, 0, n}], {n, 0, 10}]], {m, 0, 10}]

%t Table[Table[Sum[A[n, k, m], {k, 0, n}], {n, 0, 10}], {m, 0, 10}];

%K nonn,tabf,uned

%O 0,5

%A _Roger L. Bagula_, Feb 26 2009

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Last modified September 22 06:53 EDT 2020. Contains 337289 sequences. (Running on oeis4.)