A201166 Triangle read by rows: the Fibonacci triangle times Pascal's triangle (A007318).

1, 2, 1, 5, 4, 1, 12, 14, 6, 1, 31, 46, 27, 8, 1, 85, 150, 108, 44, 10, 1, 248, 493, 410, 206, 65, 12, 1, 762, 1644, 1519, 887, 348, 90, 14, 1, 2440, 5569, 5569, 3641, 1673, 542, 119, 16, 1, 8064, 19147, 20348, 14524, 7529, 2876, 796, 152, 18, 1, 27300, 66706, 74367, 56925, 32458, 14077, 4620, 1118, 189, 20, 1

Offset

0,2

Links

Table of n, a(n) for n=0..65.

Tian-Xiao He and Renzo Sprugnoli, Sequence characterization of Riordan arrays, Discrete Math. 309 (2009), no. 12, 3962-3974.

Example

Triangle begins:
1
2 1
5 4 1
12 14 6 1
31 46 27 8 1
85 150 108 44 10 1
248 493 410 206 65 12 1
...

Maple

A201166 := proc(n, k)
    add( A139375(n, j)*binomial(j, k), j=k..n) ;
end proc: # R. J. Mathar, Jul 09 2013

Mathematica

F[n_, k_] := If[k == 0, Fibonacci[n+1], k Sum[Fibonacci[i+1] Binomial[2(n-i)-k-1, n-i-1]/(n-i), {i, 0, n-k}]];
T[n_, k_] := Sum[F[n, j] Binomial[j, k], {j, k, n}];
Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Apr 02 2020 *)

Crossrefs

Cf. A007318, A139375, A201165.

Sequence in context: A103415 A054456 A096164 * A318942 A188137 A201165

Adjacent sequences: A201163 A201164 A201165 * A201167 A201168 A201169

Keyword

nonn,tabl

Author

N. J. A. Sloane, Nov 27 2011

Status

approved