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

1,1

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]

Links

Table of n, a(n) for n=1..33.

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

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]

Example

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

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).

Sequence in context: A341423 A184536 A363411 * A077207 A319790 A273623

Adjacent sequences: A089571 A089572 A089573 * A089575 A089576 A089577

Keyword

nonn,easy

Author

Alford Arnold, Dec 29 2003; extended May 04 2005

Extensions

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

Status

approved