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A172371 Cubic recursion antidiagonal triangle sequence: f(n,a) = a*f(n-2,a) + f(n-3,a). 0
0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 2, 2, 0, 1, 1, 3, 3, 2, 0, 1, 1, 4, 4, 5, 3, 0, 1, 1, 5, 5, 10, 8, 4, 0, 1, 1, 6, 6, 17, 15, 13, 5, 0, 1, 1, 7, 7, 26, 24, 34, 21, 7 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,14

COMMENTS

Row sums are {0, 1, 2, 3, 6, 10, 18, 34, 64, 128, ...}.

LINKS

Table of n, a(n) for n=0..54.

FORMULA

f(n,a) = a*f(n-2,a) + f(n-3,a);

Output(n,a) = antidiagonal(f(n,a)).

EXAMPLE

{0},

{0, 1},

{0, 1, 1},

{0, 1, 1, 1},

{0, 1, 1, 2, 2},

{0, 1, 1, 3, 3, 2},

{0, 1, 1, 4, 4, 5, 3},

{0, 1, 1, 5, 5, 10, 8, 4},

{0, 1, 1, 6, 6, 17, 15, 13, 5},

{0, 1, 1, 7, 7, 26, 24, 34, 21, 7}

MATHEMATICA

f[0, a_] := 0; f[1, a_] := 1; f[2, a_] := 1;

f[n_, a_] := f[n, a] = a*f[n - 2, a] + f[n - 3, a];

m1 = Table[f[n, a], {n, 0, 10}, {a, 1, 11}];

Table[Table[m1[[m, n - m + 1]], {m, 1, n}], {n, 1, 10}];

Flatten[%]

CROSSREFS

Sequence in context: A306910 A112185 A192062 * A279006 A112555 A108561

Adjacent sequences:  A172368 A172369 A172370 * A172372 A172373 A172374

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 01 2010

STATUS

approved

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Last modified June 20 00:47 EDT 2019. Contains 324223 sequences. (Running on oeis4.)