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 A157272 An additive three term general recursion with always even third term: Tent function(odd):f(n,m)=If[k <= Floor[n/2], 2*k + 1, 2*(n - k) + 1; 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
 1, 1, 1, 1, 7, 1, 1, 20, 20, 1, 1, 47, 155, 47, 1, 1, 102, 753, 753, 102, 1, 1, 213, 3004, 7109, 3004, 213, 1, 1, 436, 10800, 48727, 48727, 10800, 436, 1, 1, 883, 36517, 280736, 551251, 280736, 36517, 883, 1, 1, 1778, 118795, 1454163, 4879214, 4879214 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are: {1, 2, 9, 42, 251, 1712, 13545, 119928, 1187525, 12907902, 153624005,...}. With an ordinary tent function the third terms adds both even and odd values. In this case the result is fixed on only adding odd third term factors. LINKS FORMULA Tent function(odd):f(n,m)=If[k <= Floor[n/2], 2*k + 1, 2*(n - k) + 1; 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). EXAMPLE {1}, {1, 1}, {1, 7, 1}, {1, 20, 20, 1}, {1, 47, 155, 47, 1}, {1, 102, 753, 753, 102, 1}, {1, 213, 3004, 7109, 3004, 213, 1}, {1, 436, 10800, 48727, 48727, 10800, 436, 1}, {1, 883, 36517, 280736, 551251, 280736, 36517, 883, 1}, {1, 1778, 118795, 1454163, 4879214, 4879214, 1454163, 118795, 1778, 1}, {1, 3569, 376802, 7022631, 37101835, 64614329, 37101835, 7022631, 376802, 3569, 1} MATHEMATICA Clear[A, f, n, k, m]; f[n_, k_] :=If[k <= Floor[n/2], 2*k + 1, 2*(n - k) + 1; A[n_, 0, m_] := 1; A[n_, n_, 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]; Table[A[n, k, m], {m, 0, 10}, {n, 0, 10}, {k, 0, n}]; Table[Flatten[Table[Table[A[n, k, m], {k, 0, n}], {n, 0, 10}]], {m, 0, 10}] Table[Table[Sum[A[n, k, m], {k, 0, n}], {n, 0, 10}], {m, 0, 10}]; CROSSREFS Sequence in context: A154233 A174033 A119727 * A176200 A046739 A056752 Adjacent sequences:  A157269 A157270 A157271 * A157273 A157274 A157275 KEYWORD nonn,tabf,uned AUTHOR Roger L. Bagula, Feb 26 2009 STATUS approved

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Last modified October 28 13:09 EDT 2020. Contains 338055 sequences. (Running on oeis4.)