A189326 -id:A189326 - cp's OEIS frontend

A189327 Number of nondecreasing arrangements of 4 numbers in 0..n with the last equal to n and each after the second equal to the sum of one or two of the preceding four.

2, 6, 7, 12, 12, 18, 17, 24, 22, 30, 27, 36, 32, 42, 37, 48, 42, 54, 47, 60, 52, 66, 57, 72, 62, 78, 67, 84, 72, 90, 77, 96, 82, 102, 87, 108, 92, 114, 97, 120, 102, 126, 107, 132, 112, 138, 117, 144, 122, 150, 127, 156, 132, 162, 137, 168, 142, 174, 147, 180, 152, 186, 157

Offset: 1

R. H. Hardin Apr 20 2011

nonn

Row 2 of A189326

			All solutions for n=3
..0....3....1....1....1....2....1
..3....3....2....1....3....3....2
..3....3....3....2....3....3....2
..3....3....3....3....3....3....3

R. H. Hardin, Table of n, a(n) for n = 1..200

Empirical: a(n) = 2*a(n-2) -a(n-4)

A189319 Number of nondecreasing arrangements of n+2 numbers in 0..n with the last equal to n and each after the second equal to the sum of one or two of the preceding four.

Original entry on oeis.org

2, 6, 11, 32, 54, 179, 253, 866, 1161, 3234, 4100, 12289, 11179, 28957, 35448, 81956, 60820, 184122, 127607, 389213, 298758, 584334, 434068, 1773649, 705685, 1778949, 1505153, 3979185, 1735705, 7116031, 2564548, 11409548, 5647305, 10489351

Offset: 1

R. H. Hardin Apr 20 2011

nonn

Diagonal of A189326

			All solutions for n=3
..0....1....3....0....1....2....1....1....1....1....1
..3....2....3....1....3....3....1....1....2....2....1
..3....3....3....1....3....3....1....2....2....2....2
..3....3....3....2....3....3....2....3....2....3....2
..3....3....3....3....3....3....3....3....3....3....3

R. H. Hardin, Table of n, a(n) for n = 1..57

A189320 Number of nondecreasing arrangements of n+2 numbers in 0..3 with the last equal to 3 and each after the second equal to the sum of one or two of the preceding four.

Original entry on oeis.org

5, 7, 11, 16, 22, 28, 34, 40, 46, 52, 58, 64, 70, 76, 82, 88, 94, 100, 106, 112, 118, 124, 130, 136, 142, 148, 154, 160, 166, 172, 178, 184, 190, 196, 202, 208, 214, 220, 226, 232, 238, 244, 250, 256, 262, 268, 274, 280, 286, 292, 298, 304, 310, 316, 322, 328, 334, 340

Offset: 1

R. H. Hardin Apr 20 2011

nonn

Column 3 of A189326

			All solutions for n=4
..2....1....1....1....0....0....3....1....0....1....1....1....0....1....1....1
..3....2....2....1....1....1....3....3....1....1....1....2....3....1....1....1
..3....2....2....2....1....1....3....3....1....1....1....3....3....1....2....2
..3....3....2....2....2....2....3....3....1....2....2....3....3....1....2....3
..3....3....3....3....2....3....3....3....2....2....3....3....3....2....2....3
..3....3....3....3....3....3....3....3....3....3....3....3....3....3....3....3

R. H. Hardin, Table of n, a(n) for n = 1..200

Empirical: a(n) = 6*n - 8 for n>3

A189321 Number of nondecreasing arrangements of n+2 numbers in 0..4 with the last equal to 4 and each after the second equal to the sum of one or two of the preceding four.

Original entry on oeis.org

7, 12, 20, 32, 49, 70, 94, 120, 148, 178, 210, 244, 280, 318, 358, 400, 444, 490, 538, 588, 640, 694, 750, 808, 868, 930, 994, 1060, 1128, 1198, 1270, 1344, 1420, 1498, 1578, 1660, 1744, 1830, 1918, 2008, 2100, 2194, 2290, 2388, 2488, 2590, 2694, 2800, 2908

Offset: 1

R. H. Hardin, Apr 20 2011

nonn

Column 4 of A189326.

			Some solutions for n=3:
..1....1....3....0....1....2....1....1....1....4....1....0....1....1....2....1
..3....2....4....4....3....2....3....1....2....4....2....2....2....1....2....4
..4....2....4....4....3....4....3....2....3....4....3....2....2....2....2....4
..4....2....4....4....4....4....3....2....3....4....4....2....3....3....2....4
..4....4....4....4....4....4....4....4....4....4....4....4....4....4....4....4

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A189326.

Empirical: a(n) = n^2 + 11*n - 32 for n>5.

Empirical g.f.: x*(7 - 9*x + 5*x^2 + x^3 + x^4 - x^5 - x^6 - x^7) / (1 - x)^3. - Colin Barker, May 02 2018

A189322 Number of nondecreasing arrangements of n+2 numbers in 0..5 with the last equal to 5 and each after the second equal to the sum of one or two of the preceding four.

Original entry on oeis.org

8, 12, 21, 33, 54, 84, 119, 157, 195, 233, 271, 309, 347, 385, 423, 461, 499, 537, 575, 613, 651, 689, 727, 765, 803, 841, 879, 917, 955, 993, 1031, 1069, 1107, 1145, 1183, 1221, 1259, 1297, 1335, 1373, 1411, 1449, 1487, 1525, 1563, 1601, 1639, 1677, 1715

Offset: 1

R. H. Hardin, Apr 20 2011

nonn

Column 5 of A189326.

			Some solutions for n=3:
..1....1....2....5....1....1....1....1....1....4....1....2....3....2....1....0
..2....2....3....5....3....2....2....1....3....5....3....5....5....3....4....5
..2....3....3....5....3....2....3....2....4....5....4....5....5....3....4....5
..4....3....5....5....4....3....4....3....5....5....4....5....5....3....4....5
..5....5....5....5....5....5....5....5....5....5....5....5....5....5....5....5

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A189326.

Empirical: a(n) = 38*n - 147 for n>6.

Empirical g.f.: x*(8 - 4*x + 5*x^2 + 3*x^3 + 9*x^4 + 9*x^5 + 5*x^6 + 3*x^7) / (1 - x)^2. - Colin Barker, May 02 2018

A189323 Number of nondecreasing arrangements of n+2 numbers in 0..6 with the last equal to 6 and each after the second equal to the sum of one or two of the preceding four.

Original entry on oeis.org

10, 18, 36, 64, 110, 179, 275, 393, 528, 676, 836, 1008, 1192, 1388, 1596, 1816, 2048, 2292, 2548, 2816, 3096, 3388, 3692, 4008, 4336, 4676, 5028, 5392, 5768, 6156, 6556, 6968, 7392, 7828, 8276, 8736, 9208, 9692, 10188, 10696, 11216, 11748, 12292, 12848

Offset: 1

R. H. Hardin, Apr 20 2011

nonn

Column 6 of A189326.

			Some solutions for n=3:
..1....1....2....2....1....3....1....2....2....0....1....1....3....2....1....1
..5....6....3....4....4....6....5....2....4....3....3....3....3....3....5....3
..5....6....3....4....5....6....5....4....4....3....4....3....3....3....6....3
..5....6....6....4....5....6....6....6....6....3....5....4....6....3....6....6
..6....6....6....6....6....6....6....6....6....6....6....6....6....6....6....6

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A189326.

Empirical: a(n) = 6*n^2 + 34*n - 264 for n>8.

Empirical g.f.: x*(10 - 12*x + 12*x^2 + 8*x^4 + 5*x^5 + 4*x^6 - 5*x^7 - 5*x^8 - 4*x^9 - x^10) / (1 - x)^3. - Colin Barker, May 02 2018

A189324 Number of nondecreasing arrangements of n+2 numbers in 0..7 with the last equal to 7 and each after the second equal to the sum of one or two of the preceding four.

Original entry on oeis.org

11, 17, 31, 51, 91, 157, 253, 374, 509, 649, 789, 929, 1069, 1209, 1349, 1489, 1629, 1769, 1909, 2049, 2189, 2329, 2469, 2609, 2749, 2889, 3029, 3169, 3309, 3449, 3589, 3729, 3869, 4009, 4149, 4289, 4429, 4569, 4709, 4849, 4989, 5129, 5269, 5409, 5549

Offset: 1

R. H. Hardin, Apr 20 2011

nonn

Column 7 of A189326.

			Some solutions for n=3:
..1....7....2....2....1....3....3....1....1....3....1....1....1....4....1....1
..4....7....5....5....3....4....4....3....3....7....6....3....5....7....2....5
..5....7....5....5....4....7....4....4....3....7....7....4....6....7....3....6
..6....7....5....7....7....7....7....5....4....7....7....4....6....7....5....7
..7....7....7....7....7....7....7....7....7....7....7....7....7....7....7....7

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A189326.

Empirical: a(n) = 140*n - 751 for n>8.

Empirical g.f.: x*(11 - 5*x + 8*x^2 + 6*x^3 + 20*x^4 + 26*x^5 + 30*x^6 + 25*x^7 + 14*x^8 + 5*x^9) / (1 - x)^2. - Colin Barker, May 02 2018

A189325 Number of nondecreasing arrangements of n+2 numbers in 0..8 with the last equal to 8 and each after the second equal to the sum of one or two of the preceding four.

Original entry on oeis.org

13, 24, 49, 95, 179, 321, 548, 866, 1267, 1733, 2248, 2806, 3408, 4056, 4752, 5498, 6296, 7148, 8056, 9022, 10048, 11136, 12288, 13506, 14792, 16148, 17576, 19078, 20656, 22312, 24048, 25866, 27768, 29756, 31832, 33998, 36256, 38608, 41056, 43602

Offset: 1

R. H. Hardin, Apr 20 2011

nonn

Column 8 of A189326.

			Some solutions for n=3:
..2....0....1....1....2....7....2....4....3....1....0....4....1....3....3....2
..4....4....6....3....6....8....3....4....5....4....4....4....7....5....4....4
..6....4....7....4....8....8....3....4....5....4....4....4....7....5....4....4
..8....4....7....4....8....8....5....8....8....5....8....4....8....5....4....6
..8....8....8....8....8....8....8....8....8....8....8....8....8....8....8....8

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A189326.

Empirical: a(n) = (1/3)*n^3 + 10*n^2 + (587/3)*n - 1558 for n>10.

Empirical g.f.: x*(13 - 28*x + 31*x^2 - 9*x^3 + 10*x^4 + 3*x^5 + 7*x^6 - 21*x^7 - 14*x^8 - 10*x^9 + 2*x^10 + 10*x^11 + 7*x^12 + x^13) / (1 - x)^4. - Colin Barker, May 02 2018

A189328 Number of nondecreasing arrangements of 5 numbers in 0..n with the last equal to n and each after the second equal to the sum of one or two of the preceding four.

Original entry on oeis.org

2, 8, 11, 20, 21, 36, 31, 49, 42, 63, 51, 79, 60, 93, 72, 105, 80, 125, 89, 133, 104, 149, 109, 168, 117, 178, 135, 190, 138, 213, 147, 219, 166, 234, 166, 257, 176, 263, 197, 274, 196, 303, 205, 304, 227, 319, 225, 346, 234, 347, 259, 360, 254, 392, 262, 389, 290, 404

Offset: 1

R. H. Hardin, Apr 20 2011

nonn

Row 3 of A189326.

			All solutions for n=3:
..1....1....1....1....0....1....3....0....2....1....1
..2....2....3....2....1....1....3....3....3....1....1
..2....2....3....3....1....2....3....3....3....2....1
..3....2....3....3....2....3....3....3....3....2....2
..3....3....3....3....3....3....3....3....3....3....3

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A189326.

Empirical: a(n) = -3*a(n-1) -5*a(n-2) -5*a(n-3) -2*a(n-4) +3*a(n-5) +8*a(n-6) +10*a(n-7) +8*a(n-8) +3*a(n-9) -2*a(n-10) -5*a(n-11) -5*a(n-12) -3*a(n-13) -a(n-14).

Empirical g.f.: x*(2 + 14*x + 45*x^2 + 103*x^3 + 180*x^4 + 264*x^5 + 326*x^6 + 350*x^7 + 322*x^8 + 258*x^9 + 173*x^10 + 97*x^11 + 40*x^12 + 11*x^13) / ((1 - x)^2*(1 + x)^2*(1 + x^2)*(1 + x + x^2)^2*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, May 02 2018

A189329 Number of nondecreasing arrangements of 6 numbers in 0..n with the last equal to n and each after the second equal to the sum of one or two of the preceding four.

Original entry on oeis.org

2, 10, 16, 32, 33, 64, 51, 95, 76, 122, 91, 166, 102, 185, 141, 214, 137, 272, 155, 277, 201, 304, 191, 380, 199, 366, 272, 396, 237, 480, 253, 462, 335, 483, 286, 593, 299, 545, 403, 584, 335, 684, 353, 648, 465, 660, 388, 808, 395, 726, 531, 767, 435, 896, 456, 826

Offset: 1

R. H. Hardin Apr 20 2011

nonn

Row 4 of A189326

			All solutions for n=3
..1....0....1....0....1....2....0....1....1....1....1....0....1....1....1....3
..2....1....2....3....3....3....1....1....1....1....2....1....1....1....1....3
..2....1....3....3....3....3....1....2....2....1....2....1....1....1....2....3
..3....2....3....3....3....3....2....2....3....1....2....1....2....2....2....3
..3....3....3....3....3....3....2....2....3....2....3....2....3....2....3....3
..3....3....3....3....3....3....3....3....3....3....3....3....3....3....3....3

R. H. Hardin, Table of n, a(n) for n = 1..200

Empirical: a(n) = -4*a(n-1) -11*a(n-2) -24*a(n-3) -45*a(n-4) -74*a(n-5) -110*a(n-6) -149*a(n-7) -185*a(n-8) -210*a(n-9) -216*a(n-10) -196*a(n-11) -146*a(n-12) -67*a(n-13) +35*a(n-14) +149*a(n-15) +261*a(n-16) +355*a(n-17) +418*a(n-18) +440*a(n-19) +418*a(n-20) +355*a(n-21) +261*a(n-22) +149*a(n-23) +35*a(n-24) -67*a(n-25) -146*a(n-26) -196*a(n-27) -216*a(n-28) -210*a(n-29) -185*a(n-30) -149*a(n-31) -110*a(n-32) -74*a(n-33) -45*a(n-34) -24*a(n-35) -11*a(n-36) -4*a(n-37) -a(n-38)

cp's OEIS Frontend

A189327 Number of nondecreasing arrangements of 4 numbers in 0..n with the last equal to n and each after the second equal to the sum of one or two of the preceding four.

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A189319 Number of nondecreasing arrangements of n+2 numbers in 0..n with the last equal to n and each after the second equal to the sum of one or two of the preceding four.

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A189320 Number of nondecreasing arrangements of n+2 numbers in 0..3 with the last equal to 3 and each after the second equal to the sum of one or two of the preceding four.

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A189321 Number of nondecreasing arrangements of n+2 numbers in 0..4 with the last equal to 4 and each after the second equal to the sum of one or two of the preceding four.

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A189322 Number of nondecreasing arrangements of n+2 numbers in 0..5 with the last equal to 5 and each after the second equal to the sum of one or two of the preceding four.

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A189323 Number of nondecreasing arrangements of n+2 numbers in 0..6 with the last equal to 6 and each after the second equal to the sum of one or two of the preceding four.

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A189324 Number of nondecreasing arrangements of n+2 numbers in 0..7 with the last equal to 7 and each after the second equal to the sum of one or two of the preceding four.

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A189325 Number of nondecreasing arrangements of n+2 numbers in 0..8 with the last equal to 8 and each after the second equal to the sum of one or two of the preceding four.

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A189328 Number of nondecreasing arrangements of 5 numbers in 0..n with the last equal to n and each after the second equal to the sum of one or two of the preceding four.

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A189329 Number of nondecreasing arrangements of 6 numbers in 0..n with the last equal to n and each after the second equal to the sum of one or two of the preceding four.

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