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A089574
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Column 4 of an array closely related to A083480. (Both arrays have shape sequence A083479).
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10
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Columns 1 through 3 are A000124, A000330 and A086602. 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 (mathar(AT)strw.leidenuniv.nl), Jun 26 2010]
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 26 2010]
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FORMULA
| Row sums are powers of 2.
Equals A000330 + A006011 + A034263
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) = A000330(n)+A006011(n+1)+A034263(n-1) = n*(n+1)*(4*n^3+51*n^2+159*n+86)/120. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 26 2010]
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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
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CROSSREFS
| Cf. A006468, A000079.
Cf. A105552.
Cf. A000330, A006011 and A034261.
Sequence in context: A073694 A101966 A184536 * A077207 A001589 A177467
Adjacent sequences: A089571 A089572 A089573 * A089575 A089576 A089577
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KEYWORD
| nonn
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AUTHOR
| Alford Arnold (Alford1940(AT)aol.com), Dec 29 2003; extended May 04 2005
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EXTENSIONS
| Extended beyond a(8) by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 26 2010
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