A212536 -id:A212536 - cp's OEIS frontend

A212532 Number of nondecreasing sequences of n 1..4 integers with every element dividing the sequence sum.

4, 4, 7, 10, 15, 15, 24, 29, 39, 45, 57, 65, 83, 92, 111, 127, 149, 163, 193, 213, 245, 270, 305, 333, 378, 408, 455, 496, 547, 587, 650, 697, 763, 819, 889, 949, 1033, 1096, 1183, 1261, 1353, 1431, 1539, 1625, 1737, 1836, 1953, 2057, 2192, 2300, 2439, 2566, 2711

Offset: 1

R. H. Hardin, May 20 2012

nonn

Column 4 of A212536.

			Some solutions for n=8:
..1....4....2....2....1....1....1....2....1....1....1....2....3....1....1....1
..1....4....2....3....1....1....1....2....1....2....1....2....3....1....1....3
..2....4....2....3....1....2....1....4....1....2....3....2....3....1....2....3
..4....4....2....3....3....2....1....4....1....2....3....2....3....1....2....3
..4....4....4....3....3....2....1....4....1....2....4....2....3....1....2....3
..4....4....4....3....3....2....1....4....1....3....4....2....3....1....4....3
..4....4....4....3....3....2....2....4....2....3....4....4....3....3....4....4
..4....4....4....4....3....4....2....4....4....3....4....4....3....3....4....4

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A212536.

Empirical: a(n) = a(n-1) + a(n-2) - a(n-4) - a(n-5) + a(n-6) + a(n-12) - a(n-13) - a(n-14) + a(n-16) + a(n-17) - a(n-18).

Empirical g.f.: x*(4 - x^2 - x^3 + 2*x^4 - 2*x^5 + x^6 + 3*x^7 + 4*x^8 - 3*x^9 - 3*x^10 + x^11 + x^12 - x^13 + 2*x^15 - x^17) / ((1 - x)^4*(1 + x)^2*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)^2*(1 - x^2 + x^4)). - Colin Barker, Jul 20 2018

A212533 Number of nondecreasing sequences of n 1..5 integers with every element dividing the sequence sum.

Original entry on oeis.org

5, 5, 8, 12, 21, 21, 33, 40, 57, 70, 90, 101, 132, 153, 208, 262, 343, 401, 491, 546, 625, 667, 737, 770, 851, 889, 989, 1070, 1226, 1361, 1592, 1787, 2070, 2305, 2616, 2864, 3198, 3444, 3781, 4045, 4399, 4670, 5070, 5391, 5860, 6254, 6786, 7235, 7843, 8336

Offset: 1

R. H. Hardin May 20 2012

nonn

Column 5 of A212536

			Some solutions for n=8
..1....1....5....1....1....1....1....2....1....1....1....1....1....1....2....1
..1....1....5....2....1....2....2....2....1....1....1....3....1....1....3....1
..1....2....5....2....2....2....3....3....1....2....1....3....1....3....3....1
..1....4....5....3....2....5....3....3....3....2....1....3....1....5....3....1
..4....4....5....4....2....5....3....5....3....2....1....5....2....5....3....2
..4....4....5....4....2....5....4....5....3....4....1....5....2....5....3....2
..4....4....5....4....2....5....4....5....3....4....1....5....4....5....3....2
..4....4....5....4....4....5....4....5....3....4....1....5....4....5....4....2

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = a(n-1) +a(n-2) -2*a(n-5) +a(n-8) +a(n-9) -a(n-10) +a(n-60) -a(n-61) -a(n-62) +2*a(n-65) -a(n-68) -a(n-69) +a(n-70)

A212534 Number of nondecreasing sequences of n 1..6 integers with every element dividing the sequence sum.

Original entry on oeis.org

6, 6, 11, 17, 30, 40, 69, 91, 130, 166, 224, 296, 439, 606, 841, 1080, 1352, 1594, 1877, 2112, 2397, 2672, 3055, 3500, 4159, 4932, 5966, 7144, 8568, 10073, 11781, 13488, 15367, 17256, 19348, 21511, 23999, 26623, 29660, 32913, 36620, 40561, 45024, 49719

Offset: 1

R. H. Hardin May 20 2012

nonn

Column 6 of A212536

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = a(n-1) +a(n-2) -a(n-5) -a(n-6) -a(n-7) +a(n-8) +a(n-9) +a(n-10) -a(n-13) -a(n-14) +a(n-15) +a(n-60) -a(n-61) -a(n-62) +a(n-65) +a(n-66) +a(n-67) -a(n-68) -a(n-69) -a(n-70) +a(n-73) +a(n-74) -a(n-75)

A212535 Number of nondecreasing sequences of n 1..7 integers with every element dividing the sequence sum.

Original entry on oeis.org

7, 7, 12, 18, 33, 44, 83, 106, 157, 200, 272, 351, 518, 715, 1010, 1343, 1756, 2152, 2670, 3101, 3685, 4168, 4866, 5474, 6452, 7345, 8718, 10082, 11964, 13801, 16207, 18489, 21386, 24289, 27876, 31630, 36294, 41204, 47131, 53471, 60792, 68552, 77355, 86516

Offset: 1

R. H. Hardin May 20 2012

nonn

Column 7 of A212536

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

R. H. Hardin, Table of n, a(n) for n = 1..210

A212537 Number of nondecreasing sequences of 4 1..n integers with every element dividing the sequence sum.

Original entry on oeis.org

1, 3, 5, 10, 12, 17, 18, 23, 26, 30, 31, 40, 41, 43, 47, 52, 53, 59, 60, 67, 70, 72, 73, 82, 84, 86, 89, 94, 95, 103, 104, 109, 111, 113, 115, 125, 126, 128, 130, 137, 138, 144, 145, 150, 155, 157, 158, 167, 168, 172, 174, 179, 180, 186, 188, 193, 195, 197, 198, 210, 211, 213

Offset: 1

R. H. Hardin, May 20 2012

nonn

Row 4 of A212536.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A212536.

Empirical: a(n) = 2*a(n-1) -2*a(n-2) -a(n-3) +4*a(n-4) -5*a(n-5) +6*a(n-7) -9*a(n-8) +3*a(n-9) +6*a(n-10) -12*a(n-11) +7*a(n-12) +4*a(n-13) -13*a(n-14) +11*a(n-15) -11*a(n-17) +13*a(n-18) -4*a(n-19) -7*a(n-20) +13*a(n-21) -8*a(n-22) -a(n-23) +10*a(n-24) -10*a(n-25) +5*a(n-26) +5*a(n-27) -10*a(n-28) +10*a(n-29) -a(n-30) -8*a(n-31) +13*a(n-32) -7*a(n-33) -4*a(n-34) +13*a(n-35) -11*a(n-36) +11*a(n-38) -13*a(n-39) +4*a(n-40) +7*a(n-41) -12*a(n-42) +6*a(n-43) +3*a(n-44) -9*a(n-45) +6*a(n-46) -5*a(n-48) +4*a(n-49) -a(n-50) -2*a(n-51) +2*a(n-52) -a(n-53).

A212538 Number of nondecreasing sequences of 5 1..n integers with every element dividing the sequence sum.

Original entry on oeis.org

1, 4, 8, 15, 21, 30, 33, 46, 53, 66, 67, 87, 88, 95, 111, 125, 126, 143, 144, 170, 180, 183, 184, 214, 220, 223, 231, 245, 246, 282, 283, 297, 302, 305, 315, 346, 347, 350, 355, 388, 389, 412, 413, 420, 442, 445, 446, 478, 481, 495, 499, 507, 508, 526, 533, 553, 557, 560

Offset: 1

R. H. Hardin May 20 2012

nonn

Row 5 of A212536

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

R. H. Hardin, Table of n, a(n) for n = 1..210

A212539 Number of nondecreasing sequences of 6 1..n integers with every element dividing the sequence sum.

Original entry on oeis.org

1, 4, 8, 15, 21, 40, 44, 64, 76, 103, 104, 148, 149, 165, 197, 229, 230, 271, 272, 343, 362, 367, 368, 449, 457, 462, 478, 521, 522, 639, 640, 677, 685, 688, 707, 800, 801, 804, 812, 937, 938, 1011, 1012, 1026, 1094, 1097, 1098, 1204, 1208, 1241, 1246, 1262, 1263

Offset: 1

R. H. Hardin May 20 2012

nonn

Row 6 of A212536

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

R. H. Hardin, Table of n, a(n) for n = 1..210

A212540 Number of nondecreasing sequences of 7 1..n integers with every element dividing the sequence sum.

Original entry on oeis.org

1, 5, 12, 24, 33, 69, 83, 116, 145, 188, 193, 290, 293, 332, 428, 496, 497, 606, 607, 772, 840, 857, 858, 1079, 1098, 1109, 1153, 1277, 1278, 1626, 1627, 1723, 1750, 1757, 1832, 2100, 2101, 2106, 2130, 2541, 2542, 2784, 2785, 2843, 3111, 3115, 3116, 3462, 3477

Offset: 1

R. H. Hardin May 20 2012

nonn

Row 7 of A212536

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

R. H. Hardin, Table of n, a(n) for n = 1..210

A212531 Number of nondecreasing sequences of n 1..n integers with every element dividing the sequence sum.

Original entry on oeis.org

1, 2, 5, 10, 21, 40, 83, 161, 331, 644, 1102, 3627, 5646, 10083, 29188, 53681, 84121, 237453, 373114, 1400757, 2443494

Offset: 1

R. H. Hardin May 20 2012

nonn

Diagonal of A212536

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

cp's OEIS Frontend

A212532 Number of nondecreasing sequences of n 1..4 integers with every element dividing the sequence sum.

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A212533 Number of nondecreasing sequences of n 1..5 integers with every element dividing the sequence sum.

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A212534 Number of nondecreasing sequences of n 1..6 integers with every element dividing the sequence sum.

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A212535 Number of nondecreasing sequences of n 1..7 integers with every element dividing the sequence sum.

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A212537 Number of nondecreasing sequences of 4 1..n integers with every element dividing the sequence sum.

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A212538 Number of nondecreasing sequences of 5 1..n integers with every element dividing the sequence sum.

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A212539 Number of nondecreasing sequences of 6 1..n integers with every element dividing the sequence sum.

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A212540 Number of nondecreasing sequences of 7 1..n integers with every element dividing the sequence sum.

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A212531 Number of nondecreasing sequences of n 1..n integers with every element dividing the sequence sum.

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