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A109906 A triangle of coefficients based on A000045 and the Pascal's triangle: t(n,m)=Fibonacci[(n - m + 1)]*Fibonacci[(m + 1)]*Binomial[n, m]. 12
1, 1, 1, 2, 2, 2, 3, 6, 6, 3, 5, 12, 24, 12, 5, 8, 25, 60, 60, 25, 8, 13, 48, 150, 180, 150, 48, 13, 21, 91, 336, 525, 525, 336, 91, 21, 34, 168, 728, 1344, 1750, 1344, 728, 168, 34, 55, 306, 1512, 3276, 5040, 5040, 3276, 1512, 306, 55, 89, 550, 3060, 7560, 13650, 16128 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Row sums are:

{1, 2, 6, 18, 58, 186, 602, 1946, 6298, 20378, 65946}

LINKS

Reinhard Zumkeller, Rows n = 0..120 of table, flattened

Index entries for triangles and arrays related to Pascal's triangle

FORMULA

t(n,m)=Fibonacci[(n - m + 1)]*Fibonacci[(m + 1)]*Binomial[n, m].

T(n,k) = A058071(n,k) * A007318(n,k), k = 0..n. - Reinhard Zumkeller, Aug 15 2013

EXAMPLE

{1},

{1, 1},

{2, 2, 2},

{3, 6, 6, 3},

{5, 12, 24, 12, 5},

{8, 25, 60, 60, 25, 8},

{13, 48, 150, 180, 150, 48, 13},

{21, 91, 336, 525, 525, 336, 91, 21},

{34, 168, 728, 1344, 1750, 1344, 728, 168, 34},

{55, 306, 1512, 3276, 5040, 5040, 3276, 1512, 306, 55},

{89, 550, 3060, 7560, 13650, 16128, 13650, 7560, 3060, 550, 89}

MATHEMATICA

Clear[t, n, m] t[n_, m_] := Fibonacci[(n - m + 1)]*Fibonacci[(m + 1)]*Binomial[n, m]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]

PROG

(Haskell)

a109906 n k = a109906_tabl !! n !! k

a109906_row n = a109906_tabl !! n

a109906_tabl = zipWith (zipWith (*)) a058071_tabl a007318_tabl

-- Reinhard Zumkeller, Aug 15 2013

CROSSREFS

Cf. A141611, A141617, A000045.

Some other Fibonacci-Pascal triangles: A027926, A036355, A037027, A074829, A105809, A111006, A114197, A162741, A228074.

Sequence in context: A104346 A318238 A193450 * A104856 A038715 A293518

Adjacent sequences:  A109903 A109904 A109905 * A109907 A109908 A109909

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula and Gary W. Adamson, Aug 24 2008

EXTENSIONS

Offset changed by Reinhard Zumkeller, Aug 15 2013

STATUS

approved

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Last modified October 21 16:33 EDT 2018. Contains 316427 sequences. (Running on oeis4.)