A309049 -id:A309049 - cp's OEIS frontend

A326505 Number of (binary) max-heaps on n elements from the set {0,1} containing exactly four 0's.

1, 1, 2, 5, 7, 11, 17, 27, 34, 50, 65, 94, 110, 154, 182, 250, 279, 375, 420, 555, 601, 781, 847, 1085, 1152, 1456, 1547, 1932, 2024, 2500, 2620, 3204, 3325, 4029, 4182, 5025, 5179, 6175, 6365, 7535, 7726, 9086, 9317, 10890, 11122, 12926, 13202, 15262, 15539

Offset: 4

Alois P. Heinz, Jul 09 2019

Alois P. Heinz, Table of n, a(n) for n = 4..10000
Eric Weisstein's World of Mathematics, Heap
Wikipedia, Binary heap
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,1,-1,-4,4,1,-1,2,-2,-1,1).

Column k=4 of A309049.

G.f.: -x^4*(2*x^3-x^2+1)*(2*x^6-x^5-x^4+x^3+1)/((x^2+1)^2*(x+1)^4*(x-1)^5).

A326506 Number of (binary) max-heaps on n elements from the set {0,1} containing exactly five 0's.

Original entry on oeis.org

1, 1, 2, 5, 8, 13, 24, 34, 52, 74, 116, 145, 211, 270, 392, 460, 643, 767, 1062, 1197, 1618, 1843, 2464, 2702, 3550, 3920, 5096, 5481, 7029, 7596, 9648, 10232, 12853, 13677, 17034, 17877, 22060, 23209, 28424, 29594, 35960, 37510, 45276, 46849, 56167, 58202

Offset: 5

Alois P. Heinz, Jul 09 2019

Alois P. Heinz, Table of n, a(n) for n = 5..10000
Eric Weisstein's World of Mathematics, Heap
Wikipedia, Binary heap
Index entries for linear recurrences with constant coefficients, signature (1, 2, -2, 2, -2, -6, 6, 0, 0, 6, -6, -2, 2, -2, 2, 1, -1).

Column k=5 of A309049.

LinearRecurrence[{1, 2, -2, 2, -2, -6, 6, 0, 0, 6, -6, -2, 2, -2, 2, 1, -1},{1, 1, 2, 5, 8, 13, 24, 34, 52, 74, 116, 145, 211, 270, 392, 460, 643},50] (* Ray Chandler, Sep 25 2022 *)

A326507 Number of (binary) max-heaps on n elements from the set {0,1} containing exactly six 0's.

Original entry on oeis.org

1, 1, 2, 5, 9, 16, 27, 44, 68, 114, 156, 236, 325, 500, 622, 900, 1143, 1659, 1954, 2731, 3277, 4564, 5185, 7040, 8114, 10948, 12124, 16058, 17977, 23640, 25692, 33304, 36493, 46965, 50322, 64017, 69025, 87208, 92423, 115652, 123168, 153142, 160908, 198440

Offset: 6

Alois P. Heinz, Jul 09 2019

Alois P. Heinz, Table of n, a(n) for n = 6..10000
Eric Weisstein's World of Mathematics, Heap
Wikipedia, Binary heap
Index entries for linear recurrences with constant coefficients, signature (1, 2, -2, 3, -3, -8, 8, -2, 2, 12, -12, -2, 2, -8, 8, 3, -3, 2, -2, -1, 1).

Column k=6 of A309049.

LinearRecurrence[{1, 2, -2, 3, -3, -8, 8, -2, 2, 12, -12, -2, 2, -8, 8, 3, -3, 2, -2, -1, 1},{1, 1, 2, 5, 9, 16, 27, 44, 68, 114, 156, 236, 325, 500, 622, 900, 1143, 1659, 1954, 2731, 3277},50] (* Ray Chandler, Sep 25 2022 *)

A326508 Number of (binary) max-heaps on n elements from the set {0,1} containing exactly seven 0's.

Original entry on oeis.org

1, 1, 2, 5, 10, 18, 32, 54, 94, 140, 222, 329, 532, 708, 1060, 1432, 2175, 2691, 3878, 4905, 7110, 8398, 11740, 14150, 19788, 22622, 30826, 35845, 48712, 54376, 72472, 82016, 108845, 119317, 155962, 172861, 224834, 243018, 312232, 340486, 435210, 465184

Offset: 7

Alois P. Heinz, Jul 09 2019

Alois P. Heinz, Table of n, a(n) for n = 7..10000
Eric Weisstein's World of Mathematics, Heap
Wikipedia, Binary heap
Index entries for linear recurrences with constant coefficients, signature (1, 2, -2, 3, -3, -8, 8, -1, 1, 10, -10, -5, 5, 0, 0, 5, -5, -10, 10, 1, -1, 8, -8, -3, 3, -2, 2, 1, -1).

Column k=7 of A309049.

A326509 Number of (binary) max-heaps on n elements from the set {0,1} containing exactly eight 0's.

Original entry on oeis.org

1, 1, 2, 5, 11, 21, 37, 69, 109, 181, 287, 487, 695, 1079, 1547, 2451, 3194, 4742, 6321, 9522, 11736, 16858, 21262, 30782, 36420, 50928, 61596, 86402, 99282, 135682, 158874, 217130, 243959, 326783, 373076, 498819, 550809, 724803, 811051, 1064139, 1158863

Offset: 8

Alois P. Heinz, Jul 09 2019

Alois P. Heinz, Table of n, a(n) for n = 8..10000
Eric Weisstein's World of Mathematics, Heap
Wikipedia, Binary heap
Index entries for linear recurrences with constant coefficients, signature (1, 2, -2, 3, -3, -8, 8, 0, 0, 8, -8, -8, 8, 8, -8, 6, -6, -20, 20, 6, -6, 8, -8, -8, 8, 8, -8, 0, 0, -8, 8, 3, -3, 2, -2, -1, 1).

Column k=8 of A309049.

A326510 Number of (binary) max-heaps on n elements from the set {0,1} containing exactly nine 0's.

Original entry on oeis.org

1, 1, 2, 5, 12, 23, 44, 76, 131, 219, 390, 600, 971, 1469, 2424, 3328, 5090, 7138, 11160, 14397, 21237, 28018, 41944, 51464, 73734, 92806, 134244, 159128, 222578, 269926, 379520, 437776, 599719, 706183, 969590, 1095469, 1473434, 1694393, 2279460, 2532548

Offset: 9

Alois P. Heinz, Jul 09 2019

Alois P. Heinz, Table of n, a(n) for n = 9..10000
Eric Weisstein's World of Mathematics, Heap
Wikipedia, Binary heap
Index entries for linear recurrences with constant coefficients, signature (1, 2, -2, 3, -3, -8, 8, 1, -1, 6, -6, -11, 11, 16, -16, 6, -6, -28, 28, 14, -14, 0, 0, -14, 14, 28, -28, -6, 6, -16, 16, 11, -11, -6, 6, -1, 1, 8, -8, -3, 3, -2, 2, 1, -1).

Column k=9 of A309049.

A326511 Number of (binary) max-heaps on n elements from the set {0,1} containing exactly ten 0's.

Original entry on oeis.org

1, 1, 2, 5, 13, 26, 47, 86, 151, 277, 460, 783, 1248, 2136, 3091, 4872, 7166, 11610, 15720, 23832, 32847, 50788, 64714, 94916, 124296, 185246, 226976, 324586, 407824, 589416, 699010, 977912, 1188567, 1674431, 1938526, 2661055, 3147865, 4338414, 4923481

Offset: 10

Alois P. Heinz, Jul 09 2019

Alois P. Heinz, Table of n, a(n) for n = 10..10000
Eric Weisstein's World of Mathematics, Heap
Wikipedia, Binary heap
Index entries for linear recurrences with constant coefficients, signature (1, 2, -2, 3, -3, -8, 8, 2, -2, 4, -4, -14, 14, 24, -24, 5, -5, -34, 34, 25, -25, -16, 16, -20, 20, 56, -56, -20, 20, -16, 16, 25, -25, -34, 34, 5, -5, 24, -24, -14, 14, 4, -4, 2, -2, -8, 8, 3, -3, 2, -2, -1, 1).

Column k=10 of A309049.

b:= proc(n) option remember; series(`if`(n=0, 1, (g-> (f->
      x^n+b(f)*b(n-1-f))(min(g-1, n-g/2)))(2^ilog2(n))), x, 11)
    end:
a:= n-> coeff(b(n), x, 10):
seq(a(n), n=10..50);

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A326505 Number of (binary) max-heaps on n elements from the set {0,1} containing exactly four 0's.

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A326506 Number of (binary) max-heaps on n elements from the set {0,1} containing exactly five 0's.

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A326507 Number of (binary) max-heaps on n elements from the set {0,1} containing exactly six 0's.

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A326508 Number of (binary) max-heaps on n elements from the set {0,1} containing exactly seven 0's.

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A326509 Number of (binary) max-heaps on n elements from the set {0,1} containing exactly eight 0's.

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A326510 Number of (binary) max-heaps on n elements from the set {0,1} containing exactly nine 0's.

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A326511 Number of (binary) max-heaps on n elements from the set {0,1} containing exactly ten 0's.

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