A023531 -id:A023531 - cp's OEIS frontend

A023563 Convolution of A023531 and A000201.

0, 1, 3, 4, 7, 11, 13, 17, 21, 26, 31, 35, 41, 47, 53, 59, 66, 73, 79, 86, 95, 102, 111, 119, 126, 136, 144, 154, 163, 173, 184, 193, 202, 212, 223, 235, 245, 257, 270, 279, 291, 302, 313, 327, 339, 351, 366, 378, 391, 403, 416, 431, 443, 456, 471

Offset: 1

Clark Kimberling

nonn

A023564 Convolution of A023531 and A001950.

Original entry on oeis.org

0, 2, 5, 7, 12, 18, 22, 28, 35, 43, 51, 58, 67, 77, 87, 97, 108, 119, 129, 141, 155, 167, 181, 194, 206, 221, 235, 251, 266, 282, 299, 314, 329, 345, 363, 382, 399, 418, 438, 454, 473, 491, 509, 531, 551, 571, 594, 614, 635, 655, 676, 699, 719

Offset: 1

Clark Kimberling

nonn

A023566 Convolution of A023531 and A014306.

Original entry on oeis.org

0, 0, 1, 1, 0, 2, 2, 1, 2, 3, 2, 2, 3, 2, 4, 4, 3, 3, 4, 4, 4, 5, 3, 4, 5, 5, 5, 5, 5, 5, 6, 6, 5, 6, 6, 5, 7, 6, 5, 7, 7, 7, 6, 6, 8, 7, 7, 7, 8, 8, 8, 8, 7, 6, 9, 9, 7, 9, 9, 8, 8, 9, 7, 8, 9, 10, 10, 9, 8, 10, 10, 10, 9, 9, 9, 10, 10, 10, 11, 10, 11, 10, 11, 10, 10, 10, 11, 9, 11, 10

Offset: 1

Clark Kimberling

nonn

A023858 a(n) = 1t(n) + 2t(n-1) + ... + k*t(n+1-k), where k = floor((n+1)/2), t = A023531.

Original entry on oeis.org

0, 1, 2, 0, 1, 2, 3, 4, 6, 2, 3, 4, 5, 7, 9, 11, 13, 5, 6, 8, 10, 12, 14, 16, 18, 20, 23, 11, 13, 15, 17, 19, 21, 23, 26, 29, 32, 35, 38, 20, 22, 24, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 66, 70, 74, 78, 82, 50, 53, 56, 59, 62, 65, 68, 72, 76, 80, 84, 88, 92

Offset: 1

Clark Kimberling

nonn

Array[Sum[k Boole@ IntegerQ@ Sqrt[8 # + 9] &[# + 1 - k], {k, Floor[(# + 1)/2]}] &, 82] (* Michael De Vlieger, Jun 12 2019 *)

a(n) = Sum_{k=1..floor((n+1)/2)} A023531(n+1-k). - Sean A. Irvine, Jun 11 2019

Missing a(21)=10 inserted and title simplified by Sean A. Irvine, Jun 11 2019

A024307 a(n) = 2t(n) + 3t(n-1) + ... + (k+1)*t(n+1-k), where k=floor((n+1)/2) and t = A023531.

Original entry on oeis.org

0, 2, 3, 0, 2, 3, 4, 5, 8, 3, 4, 5, 6, 9, 11, 13, 15, 6, 7, 10, 12, 14, 16, 18, 20, 22, 26, 13, 15, 17, 19, 21, 23, 25, 29, 32, 35, 38, 41, 22, 24, 26, 28, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 70, 74, 78, 82, 86, 53, 56, 59, 62, 65, 68, 71, 76, 80, 84

Offset: 1

Clark Kimberling

nonn

a(n) = Sum_{k=1..floor((n+1)/2)} (k+1) * A023531(n+1-k). - Sean A. Irvine, Jun 26 2019

a(64) corrected and title simplified by Sean A. Irvine, Jun 26 2019

A024855 a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = [ n/2 ], s = (natural numbers), t = A023531.

Original entry on oeis.org

1, 0, 0, 1, 2, 3, 4, 1, 2, 3, 4, 5, 7, 9, 11, 4, 5, 6, 8, 10, 12, 14, 16, 18, 20, 9, 11, 13, 15, 17, 19, 21, 23, 26, 29, 32, 35, 18, 20, 22, 24, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 66, 70, 74, 78, 47, 50, 53, 56, 59, 62, 65, 68, 72, 76, 80

Offset: 2

Clark Kimberling

nonn

Cf. A023531.

A024870 a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = [ n/2 ], s = (natural numbers >= 2), t = A023531.

Original entry on oeis.org

2, 0, 0, 2, 3, 4, 5, 2, 3, 4, 5, 6, 9, 11, 13, 5, 6, 7, 10, 12, 14, 16, 18, 20, 22, 11, 13, 15, 17, 19, 21, 23, 25, 29, 32, 35, 38, 20, 22, 24, 26, 28, 32, 35, 38, 41, 44, 47, 50, 53, 56, 31, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 70, 74, 78, 82, 50, 53, 56, 59, 62, 65, 68, 71, 76, 80, 84, 88

Offset: 2

Clark Kimberling

nonn

A024879 a(n) = s(1)s(n) + s(2)s(n-1) + ... + s(k)s(n-k+1), where k = [ n/2 ], s = A023531.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 2, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 2, 0, 0, 0, 0, 3, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 2, 0, 1, 0, 0, 2, 1, 0, 1, 1

Offset: 2

Clark Kimberling

nonn

A024882 a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = [ n/2 ], s = A023531, t = (Lucas numbers).

Original entry on oeis.org

0, 0, 4, 7, 11, 18, 29, 47, 94, 152, 246, 398, 644, 1042, 1686, 2728, 4537, 7341, 11878, 19219, 31097, 50316, 81413, 131729, 213142, 344871, 559377, 905091, 1464468, 2369559, 3834027, 6203586

Offset: 2

Clark Kimberling

nonn

A024884 a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = [ n/2 ], s = A023531, t = (composite numbers).

Original entry on oeis.org

0, 0, 8, 9, 10, 12, 14, 15, 28, 32, 35, 37, 40, 44, 46, 48, 69, 73, 77, 81, 85, 89, 93, 96, 100, 104, 133, 139, 144, 148, 154, 162, 166, 170, 176, 181, 187, 191, 229, 236, 242, 248, 255, 262, 268, 275, 281, 287, 294, 301, 308, 314, 361, 370, 380, 386, 394, 401, 408, 418, 425

Offset: 2

Clark Kimberling

nonn

cp's OEIS Frontend

A023563 Convolution of A023531 and A000201.

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Author

Keywords

A023564 Convolution of A023531 and A001950.

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Author

Keywords

A023566 Convolution of A023531 and A014306.

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Author

Keywords

A023858 a(n) = 1*t(n) + 2*t(n-1) + ... + k*t(n+1-k), where k = floor((n+1)/2), t = A023531.

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Programs

Mathematica

Formula

Extensions

A024307 a(n) = 2*t(n) + 3*t(n-1) + ... + (k+1)*t(n+1-k), where k=floor((n+1)/2) and t = A023531.

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Author

Keywords

Formula

Extensions

A024855 a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = [ n/2 ], s = (natural numbers), t = A023531.

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Crossrefs

A024870 a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = [ n/2 ], s = (natural numbers >= 2), t = A023531.

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Author

Keywords

A024879 a(n) = s(1)s(n) + s(2)s(n-1) + ... + s(k)s(n-k+1), where k = [ n/2 ], s = A023531.

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Author

Keywords

A024882 a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = [ n/2 ], s = A023531, t = (Lucas numbers).

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Author

Keywords

A024884 a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = [ n/2 ], s = A023531, t = (composite numbers).

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Author

Keywords

A023858 a(n) = 1t(n) + 2t(n-1) + ... + k*t(n+1-k), where k = floor((n+1)/2), t = A023531.

A024307 a(n) = 2t(n) + 3t(n-1) + ... + (k+1)*t(n+1-k), where k=floor((n+1)/2) and t = A023531.