A107600 Column 5 of array illustrated in A089574 and related to A034261.

1, 18, 101, 357, 978, 2274, 4711, 8954, 15915, 26806, 43197, 67079, 100932, 147798, 211359, 296020, 406997, 550410, 733381, 964137, 1252118, 1608090, 2044263, 2574414, 3214015, 3980366, 4892733, 5972491, 7243272, 8731118, 10464639

Offset: 9

Author

Alford Arnold, May 17 2005

Keywords

• easy
• nonn

Comments

The sequences in A089574 count ordered partitions. Sequence A001296 can be associated with 9 = 3+3+3. Six times sequence A005585, associated with 10 = 3+3+2+2. The other three sequences comprising A107600 are generated in A034261 and can be associated with 10 = 5 + 5 = 4 + 4 + 2 = 2 + 2 + 2 + 2 + 2.

Examples

			A107600(n) can be constructed from five other sequences as follows:
1...7...25...65...140.......A001296
....1...11...56...196.......A034264
....6...42..162...462.......6.*.A005585.
....3...18...60...150.......A006011
....1....5...14....30.......A000330
therefore
1..18..101..357...978.......A107600
		

Links

• Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

Crossrefs

Cf. A034261, A089574, A000330, A001296, A005585, A006011, A034264.

Programs

Maple

a:= n-> `if` (n<9, 0, (92292 +(-6580 +(-5745 +(1535 +(-147+5*n) *n) *n) *n) *n) *n /720 -218): seq(a(n), n=9..45); # Alois P. Heinz, Nov 06 2009

Mathematica

Select[CoefficientList[Series[(x^5-5x^4+7x^3+4x^2-11x-1)x^9/(x-1)^7, {x,0,50}],x],#>0&] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1}, {1,18,101,357,978,2274,4711},42] (* Harvey P. Dale, May 01 2011 *)

Formula

G.f.: (x^5 -5*x^4 +7*x^3 +4*x^2 -11*x -1) *x^9 /(x-1)^7. - Alois P. Heinz, Nov 06 2009

Extensions

More terms from Alois P. Heinz, Nov 06 2009