A089574 Column 4 of an array closely related to A083480. (Both arrays have shape sequence A083479).

5, 32, 113, 299, 664, 1309, 2366, 4002, 6423, 9878, 14663, 21125, 29666, 40747, 54892, 72692, 94809, 121980, 155021, 194831, 242396, 298793, 365194, 442870, 533195, 637650, 757827, 895433, 1052294, 1230359, 1431704, 1658536, 1913197

Offset: 1

Author

Alford Arnold, Dec 29 2003; extended May 04 2005

Keywords

• nonn
• easy

Comments

The diagonals are finite and sum to A047970.

Values appear to be a transformation of A006468 (rooted planar maps). Also known as well-labeled trees (cf. A000168).

First differences of the conjectured polynomial formula for A006468. [From R. J. Mathar, Jun 26 2010]

Examples

			The array begins
1
2
4
7 1
11 5
16 14 2
22 30 12
29 55 39 5
37 91 95 32 1
		

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A105552, A006468.

Cf. A006011, A034261.

Cf. A000124 (column 1), A000330 (column 2), A086602 (column 3), A107600 (column 5), A107601 (column 6), A109125 (column 7), A109126 (column 8), A109820 (column 9), A108538 (column 10), A109821 (column 11), A110553 (column 12), A110624 (column 13).

Formula

Row sums are powers of 2.

a(n) = A000330(n) + A006011(n+1) + A034263(n-1).

a(n)= +6*a(n-1) -15*a(n-2) +20*a(n-3) -15*a(n-4) +6*a(n-5) -a(n-6). G.f.: x*(5+2*x-4*x^2+x^3)/(x-1)^6. a(n) = n*(n+1)*(4*n^3+51*n^2+159*n+86)/120. [From R. J. Mathar, Jun 26 2010]

Extensions

Extended beyond a(8) by R. J. Mathar, Jun 26 2010