A064865 -id:A064865 - cp's OEIS frontend

A065229 Fill a triangular array by rows by writing numbers 1 up to b(0), 1 up to b(1), etc., where b(n) are the pentagonal numbers. The first elements of the rows form a(n).

1, 1, 3, 1, 5, 10, 4, 11, 19, 6, 16, 27, 4, 17, 31, 46, 11, 28, 46, 65, 15, 36, 58, 81, 13, 38, 64, 91, 2, 31, 61, 92, 124, 12, 46, 81, 117, 154, 16, 55, 95, 136, 178, 11, 55, 100, 146, 193, 241, 43, 93, 144, 196, 249, 16, 71, 127, 184, 242, 301, 31, 92, 154, 217, 281, 346

Offset: 0

Floor van Lamoen, Oct 22 2001

Mini-index to these sequences: A064766, A064865, A064866, A065221-A655234 are all of the same type. See A064766 for a detailed explanation.

A065230 Fill a triangular array by rows by writing numbers 1 up to b(0), 1 up to b(1), etc., where b(n) are the hexagonal numbers. The first elements of the rows form a(n).

Original entry on oeis.org

1, 1, 3, 6, 4, 9, 15, 7, 15, 24, 6, 17, 29, 42, 11, 26, 42, 59, 11, 30, 50, 71, 2, 25, 49, 74, 100, 7, 35, 64, 94, 125, 4, 37, 71, 106, 142, 179, 27, 66, 106, 147, 189, 1, 45, 90, 136, 183, 231, 4, 54, 105, 157, 210, 264, 319, 50, 107, 165, 224, 284, 345, 29, 92, 156, 221

Offset: 0

Floor van Lamoen, Oct 22 2001

Mini-index to these sequences: A064766, A064865, A064866, A065221-A655234 are all of the same type. See A064766 for a detailed explanation.

A065231 Fill a triangular array by rows by writing numbers 1 up to b(0), 1 up to b(1), etc., where b(n) are the heptagonal numbers (A000566). The first elements of the rows form a(n).

Original entry on oeis.org

1, 1, 3, 6, 3, 8, 14, 3, 11, 20, 30, 7, 19, 32, 46, 6, 22, 39, 57, 76, 15, 36, 58, 81, 105, 18, 44, 71, 99, 128, 10, 41, 73, 106, 140, 175, 22, 59, 97, 136, 176, 217, 24, 67, 111, 156, 202, 249, 11, 60, 110, 161, 213, 266, 320, 33, 89, 146, 204, 263, 323, 384, 43, 106

Offset: 0

Floor van Lamoen, Oct 22 2001

Mini-index to these sequences: A064766, A064865, A064866, A065221-A655234 are all of the same type. See A064766 for a detailed explanation.

A065232 Fill a triangular array by rows by writing numbers 1 up to b(0), 1 up to b(1), etc., where b(n) are the octagonal numbers. The first elements of the rows form a(n).

Original entry on oeis.org

1, 1, 3, 6, 2, 7, 13, 20, 7, 16, 26, 37, 9, 22, 36, 51, 2, 19, 37, 56, 76, 1, 23, 46, 70, 95, 121, 15, 43, 72, 102, 133, 165, 22, 56, 91, 127, 164, 202, 16, 56, 97, 139, 182, 226, 271, 37, 84, 132, 181, 231, 282, 334, 46, 100, 155, 211, 268, 326, 385, 37, 98, 160

Offset: 0

Floor van Lamoen, Oct 22 2001

Mini-index to these sequences: A064766, A064865, A064866, A065221-A655234 are all of the same type. See A064766 for a detailed explanation.

A065233 Fill a triangular array by rows by writing numbers 1 up to b(0), 1 up to b(1), etc., where the b(n) are the nonzero 9-gonal (nonagonal) numbers 1, 9, 24, 46, ... (A001106). The initial elements of the rows form a(n).

Original entry on oeis.org

1, 1, 3, 6, 1, 6, 12, 19, 3, 12, 22, 33, 45, 12, 26, 41, 57, 74, 17, 36, 56, 77, 99, 11, 35, 60, 86, 113, 141, 16, 46, 77, 109, 142, 176, 7, 43, 80, 118, 157, 197, 238, 19, 62, 106, 151, 197, 244, 292, 16, 66, 117, 169, 222, 276, 331, 387, 48, 106, 165, 225, 286, 348

Offset: 0

Floor van Lamoen, Oct 22 2001

			The triangle begins as follows (the slashes indicate the numbers b(0), b(1), b(2), ...):
1/
1 2
3 4 5
6 7 8 9/
1 2 3 4 5
6 7 8 9 10 11
12 13 14 15 16 17 18
19 20 21 22 23 24/ 1 2
3 4 ...
The initial terms in the rows give the sequence 1, 1, 3, 6, 1, 6, ...

Cf. A064766 (based on the triangular numbers), A064865 (the squares).

Mini-index to these sequences: A064766, A064865, A064866, A065221-A655234 are all of the same type. See A064766 for a detailed explanation.

Module[{nn=20,p9},p9=Flatten[Range[#]&/@PolygonalNumber[9,Range[nn]]];TakeList[p9,Range[Floor[(Sqrt[1+8Length[p9]]-1)/2]]]][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 04 2020 *)

Edited by N. J. A. Sloane, Jun 03 2020

A065234 Fill a triangular array by rows by writing numbers 1 up to b(0), 1 up to b(1), etc., where b(n) are the decagonal numbers. The first elements of the rows form a(n).

Original entry on oeis.org

1, 1, 3, 6, 10, 5, 11, 18, 26, 8, 18, 29, 41, 2, 16, 31, 47, 64, 82, 16, 36, 57, 79, 102, 126, 25, 51, 78, 106, 135, 165, 21, 53, 86, 120, 155, 191, 228, 34, 73, 113, 154, 196, 239, 283, 31, 77, 124, 172, 221, 271, 322, 4, 57, 111, 166, 222, 279, 337, 396, 5, 66, 128

Offset: 0

Floor van Lamoen, Oct 22 2001

Mini-index to these sequences: A064766, A064865, A064866, A065221-A655234 are all of the same type. See A064766 for a detailed explanation.

cp's OEIS Frontend

A065229 Fill a triangular array by rows by writing numbers 1 up to b(0), 1 up to b(1), etc., where b(n) are the pentagonal numbers. The first elements of the rows form a(n).

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A065230 Fill a triangular array by rows by writing numbers 1 up to b(0), 1 up to b(1), etc., where b(n) are the hexagonal numbers. The first elements of the rows form a(n).

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A065231 Fill a triangular array by rows by writing numbers 1 up to b(0), 1 up to b(1), etc., where b(n) are the heptagonal numbers (A000566). The first elements of the rows form a(n).

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A065232 Fill a triangular array by rows by writing numbers 1 up to b(0), 1 up to b(1), etc., where b(n) are the octagonal numbers. The first elements of the rows form a(n).

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A065233 Fill a triangular array by rows by writing numbers 1 up to b(0), 1 up to b(1), etc., where the b(n) are the nonzero 9-gonal (nonagonal) numbers 1, 9, 24, 46, ... (A001106). The initial elements of the rows form a(n).

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A065234 Fill a triangular array by rows by writing numbers 1 up to b(0), 1 up to b(1), etc., where b(n) are the decagonal numbers. The first elements of the rows form a(n).

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