A110361 A triangle of coefficients based on A000931 and A000045: a(n) = a(n - 2) + a(n - 3); t(n,m) := a(n - m + 1)*a(m + 1)*Fibonacci[(n - m + 1)]*Fibonacci[(m + 1)].

1, 1, 1, 4, 1, 4, 6, 4, 4, 6, 15, 6, 16, 6, 15, 32, 15, 24, 24, 15, 32, 65, 32, 60, 36, 60, 32, 65, 147, 65, 128, 90, 90, 128, 65, 147, 306, 147, 260, 192, 225, 192, 260, 147, 306, 660, 306, 588, 390, 480, 480, 390, 588, 306, 660, 1424, 660, 1224, 882, 975, 1024, 975, 882

Offset

1,4

Comments

Row sums are:

{1, 2, 9, 20, 58, 142, 350, 860, 2035, 4848, 11354}.

Links

Table of n, a(n) for n=1..63.

Formula

a(n) = a(n - 2) + a(n - 3); t(n,m) := a(n - m + 1)*a(m + 1)*Fibonacci[(n - m + 1)]*Fibonacci[(m + 1)].

Example

{1},
{1, 1},
{4, 1, 4},
{6, 4, 4, 6},
{15, 6, 16, 6, 15},
{32, 15, 24, 24, 15, 32},
{65, 32, 60, 36, 60, 32, 65},
{147, 65, 128, 90, 90, 128, 65, 147},
{306, 147, 260, 192, 225, 192, 260, 147, 306},
{660, 306, 588, 390, 480, 480, 390, 588, 306, 660},
{1424, 660, 1224, 882, 975, 1024, 975, 882, 1224, 660, 1424}

Mathematica

Clear[t, a, n, m] a[0] = 1; a[1] = 1; a[2] = 1; a[n_] := a[n] = a[n - 2] + a[n - 3]; t[n_, m_] := a[(n - m + 1)]*a[(m + 1)]*Fibonacci[(n - m + 1)]*Fibonacci[(m + 1)]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]

Crossrefs

Cf. A141611, A141617, A000931, A000045, A058071.

Sequence in context: A167431 A205848 A297701 * A193750 A092856 A051006

Adjacent sequences: A110358 A110359 A110360 * A110362 A110363 A110364

Keyword

nonn,tabl

Author

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

Status

approved