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 A157277 Even only third term general recursion triangle sequence: Tent even function:f(n,k)=If[k <= Floor[n/2], 2*k, 2*(n - k)]; Recursion function:m=2; 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). 1

%I

%S 1,1,1,1,10,1,1,39,39,1,1,128,470,128,1,1,397,3558,3558,397,1,1,1206,

%T 22387,55452,22387,1206,1,1,3635,128377,632343,632343,128377,3635,1,1,

%U 10924,698788,6107192,12269406,6107192,698788,10924,1,1,32793,3686880

%N Even only third term general recursion triangle sequence: Tent even function:f(n,k)=If[k <= Floor[n/2], 2*k, 2*(n - k)]; Recursion function:m=2; 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, 12, 80, 728, 7912, 102640, 1528712, 25903216, 489632080, 10250405568,...}.

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

%F Recursion function:m=2;

%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, 10, 1},

%e {1, 39, 39, 1},

%e {1, 128, 470, 128, 1},

%e {1, 397, 3558, 3558, 397, 1},

%e {1, 1206, 22387, 55452, 22387, 1206, 1},

%e {1, 3635, 128377, 632343, 632343, 128377, 3635, 1},

%e {1, 10924, 698788, 6107192, 12269406, 6107192, 698788, 10924, 1},

%e {1, 32793, 3686880, 53375112, 187721254, 187721254, 53375112, 3686880, 32793, 1},

%e {1, 98402, 19079273, 437314440, 2481082814, 4375255708, 2481082814, 437314440, 19079273, 98402, 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,tabl,uned

%O 0,5

%A _Roger L. Bagula_, Feb 26 2009

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Last modified May 14 19:53 EDT 2021. Contains 343903 sequences. (Running on oeis4.)