A105552 -id:A105552 - cp's OEIS frontend

A110554 Column 11 of table A105552.

56, 285, 954, 2366, 4711, 7936, 11712, 15448, 18450, 20155, 20329, 19078, 16746, 13780, 10644, 7712, 5235, 3325, 1970, 1081, 544, 247, 99, 33, 8, 1

Offset: 1

Alford Arnold, Jul 30 2005

A105552 is constructed by summing values from ordered Gaussian polynomials, therefore the present begins with one value each from the following diagonal sequences and sums to A047970(11).

			a(6) = A107601(6) = 7936.

Cf. A047969, A047970, A110553.

Cf. A000124, A000330, A086602, A089574, A107600, A107601, A109125, A109126, A109820, A108538, A109821, A110553, A110624.

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

Original entry on oeis.org

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

Alford Arnold, Dec 29 2003; extended May 04 2005

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]

			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

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

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).

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]

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

A109125 Column 7 of array illustrated in A089574 and related to A034261.

Original entry on oeis.org

2, 41, 292, 1283, 4253, 11712, 28261, 61738, 124763, 236762, 426557, 735616, 1222064, 1965563, 3073176, 4686337, 6989056, 10217495, 14671058, 20725145, 28845727, 39605906, 53704631, 71987748, 95471569, 125369152, 163119491

Offset: 0

Alford Arnold, Jun 19 2005

			a(1) = 2 because 4+4+4 and 3+3+3+3 cannot be permuted. a(2) = 41 because there are 3 + 7 + 12 + 9 + 10 ways of permuting the associated partitions.
5553 (3 ways), 4441 & 544 (4+3 ways), 4432 (12 ways), 33331 & 4333 (5 + 4 ways) and 33322 (in 10 ways).

Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1). [From _R. J. Mathar_, Jun 26 2010]

Cf. A000124, A000330, A034261, A086602, A089574, A107601.

LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{2,41,292,1283,4253,11712,28261,61738,124763},30] (* Harvey P. Dale, Aug 21 2024 *)

From R. J. Mathar, Jun 26 2010: (Start)
a(n) = A105552(11+n,5+n).
G.f.: x*(-2-23*x+5*x^2+37*x^3-26*x^4-9*x^5+17*x^6-7*x^7+x^8)/(x-1)^9. a(n) = -1+1277*n/840 -19*n^3/480 -67*n^2/480 +41*n^5/80 +257*n^6/2800 +23*n^7/3360 +6049*n^4/5760 +n^8/5760. (End)

Extended beyond a(6) by R. J. Mathar, Jun 26 2010

A109820 Column 9 of array illustrated in A089574 and related to A034261.

Original entry on oeis.org

6, 126, 992, 4921, 18450, 57198, 154420, 375106, 838075, 1749221, 3449895, 6485363, 11699374, 20362113, 34340211, 56319046, 90089305, 140911696, 215975810, 324971445, 480793226, 700402096, 1005870222, 1425639066, 1996023823, 2763001135, 3784320961, 5131987727, 6895160406, 9183525995, 12131205973

Offset: 0

Alford Arnold, Jul 03 2005

			The associated sequences begin for n = 15 through 19:
........................1.......5
........................3.......18
................3.......18......60
........3.......18......60......150
1.......7.......25......65......140
........................6.......42
................12......84......324
........12......84......324.....924
........6.......42......162.....462
4.......32......132.....392.....952
........................10......80
................30......240.....1050
........10......90......420.....1400
........30......240.....1050....3360
1.......11......56......196.....546
........................15......135
................60......540.....2640
........15......165.....900.....3420
........................21......210
................35......385.....2205
........................28......308
........................1.......19
therefore this sequence begins
6 126 992 4921 18450

Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Cf. A109126.

Cf. A000330 (column 2), A086602 (column 3), A089574 (column 4), 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).

G.f. 6 -x*( 126 -394*x +939*x^2 -1911*x^3 +2803*x^4 -2825*x^5 +1964*x^6 -939*x^7 +298*x^8 -57*x^9 +5*x^10)/(x-1)^11 . - R. J. Mathar, Aug 28 2018

More terms with the program of A105552 from R. J. Mathar, Aug 28 2018

A109126 Column 8 of array illustrated in A089574 and related to A034261.

Original entry on oeis.org

18, 207, 1198, 4825, 15448, 42168, 102297, 226530, 466357, 904352, 1668083, 2948502, 5023797, 8289819, 13298336, 20804513, 31825172, 47709549, 70224436, 101655775, 144928958, 203750282, 282772211, 387785308, 525939919, 706000918, 938639057, 1236762708, 1615894035, 2094593893

Offset: 0

Alford Arnold, Jun 22 2005

			The associated partitions begin (for n = 14, 15, 16, ...
................1.......5.......14
................3.......18......60
........3.......18......60......150
3.......18......60......150.....315
................6.......42......162
........12......84......324.....924
4.......32......132.....392.....952
6.......42......162.....462.....1092
................10......80......350
........30......240.....1050....3360
5.......50......245.....840.....2310
................15......135.....660
........20......200.....1040....3840
................21......210.....1134
................1.......17......125
therefore this sequence begins
18 207 1198 4825 15448 ...

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Cf. A105552, A000330 (column 2), A086602 (column 3), A089574 (column 4), A107600 (column 5), A107601 (column 6), A109125 (column 7), A109820 (column 9), A108538 (column 10), A109821 (column 11), A110553 (column 12), A110624 (column 13).

G.f. ( 18+27*x -62*x^2 +48*x^4 -13*x^5 -27*x^6 +24*x^7 -8*x^8 +x^9 ) / (x-1)^10 . - R. J. Mathar, Aug 28 2018

More terms with the program of A105552 from R. J. Mathar, Aug 28 2018

A125108 Column sums of a Gaussian polynomial-shaped array. Row sums generate the Eulerian array A008292.

Original entry on oeis.org

1, 2, 4, 10, 26, 72, 202, 580

Offset: 1

Alford Arnold, Dec 25 2006

Column sums of the Gaussian polynomial template count numeric partitions. Row sums of the Gaussian polynomial template generate Pascal's triangle. A105552 has the same shape as the template and counts compositions. Row sums of the Eulerian array counts permutations of n object.

			The column sums begin 1 2 4 10 26 72 202 580 ... because the structure of the Array begin as follows:
1..................................................................
......1............................................................
......1............................................................
............1......................................................
............2......2...............................................
............1......................................................
..................1................................................
..................3......5......3..................................
..................3......5......3..................................
..................1................................................
............................1......................................
............................4.......9.......9.......4..............
............................6.......16......22......16.......6.....
............................4.......9.......9.......4..............
............................1......................................
etc.

Cf. A000041, A000079, A000142, A007318, A008292, A047970, A060351, A105552.

cp's OEIS Frontend

A110554 Column 11 of table A105552.

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

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A109125 Column 7 of array illustrated in A089574 and related to A034261.

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A109820 Column 9 of array illustrated in A089574 and related to A034261.

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A109126 Column 8 of array illustrated in A089574 and related to A034261.

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A125108 Column sums of a Gaussian polynomial-shaped array. Row sums generate the Eulerian array A008292.

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