cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A281868 Number of sets of exactly eight positive integers <= n having a square element sum.

Original entry on oeis.org

1, 1, 3, 13, 34, 86, 197, 405, 786, 1446, 2532, 4263, 6938, 10953, 16837, 25281, 37165, 53605, 75999, 106075, 145951, 198199, 265921, 352825, 463320, 602609, 776797, 993007, 1259503, 1585839, 1983013, 2463629, 3042066, 3734648, 4559849, 5538527, 6694180
Offset: 8

Views

Author

Alois P. Heinz, Feb 01 2017

Keywords

Examples

			a(8) = 1: {1,2,3,4,5,6,7,8}.
a(10) = 3: {1,2,3,4,5,6,7,8}, {1,3,5,6,7,8,9,10}, {2,3,4,6,7,8,9,10}.

Links

Crossrefs

Column k=8 of A281871.

Programs

  • Maple
    b:= proc(n, i, t) option remember;
      `if`(i(t+1)*(2*i-t)/2, 0,
      `if`(i>n, 0, b(n-i, i-1, t-1))+b(n, i-1, t))))
    end:
a:= proc(n) option remember; `if`(n<0, 0, a(n-1)+add(
       b(j^2-n, n-1, 7), j=isqrt(n-28)..isqrt(8*n-28)))
    end:
seq(a(n), n=8..60);

A281869 Number of sets of exactly nine positive integers <= n having a square element sum.

Original entry on oeis.org

0, 1, 3, 14, 47, 121, 296, 660, 1358, 2646, 4905, 8704, 14887, 24649, 39651, 62175, 95286, 143038, 210732, 305210, 435195, 611697, 848494, 1162662, 1575195, 2111713, 2803273, 3687272, 4808464, 6220104, 7985229, 10178073, 12885638, 16209468, 20267579, 25196567
Offset: 9

Views

Author

Alois P. Heinz, Feb 01 2017

Keywords

Examples

			a(10) = 1: {1,2,3,4,5,7,8,9,10}.
a(11) = 3: {1,2,3,4,5,6,7,10,11}, {1,2,3,4,5,6,8,9,11}, {1,2,3,4,5,7,8,9,10}.

Links

Crossrefs

Column k=9 of A281871.

Programs

  • Maple
    b:= proc(n, i, t) option remember;
      `if`(i(t+1)*(2*i-t)/2, 0,
      `if`(i>n, 0, b(n-i, i-1, t-1))+b(n, i-1, t))))
    end:
a:= proc(n) option remember; `if`(n<0, 0, a(n-1)+add(
       b(j^2-n, n-1, 8), j=isqrt(n-36)..isqrt(9*n-36)))
    end:
seq(a(n), n=9..60);

A281870 Number of sets of exactly ten positive integers <= n having a square element sum.

Original entry on oeis.org

0, 1, 5, 16, 58, 171, 434, 1030, 2259, 4645, 9071, 16927, 30354, 52586, 88351, 144425, 230347, 359329, 549338, 824505, 1216843, 1768278, 2533124, 3581117, 5000891, 6904149, 9430598, 12753622, 17086885, 22692075, 29887626, 39058827, 50669397, 65274492, 83535475
Offset: 10

Views

Author

Alois P. Heinz, Feb 01 2017

Keywords

Examples

			a(11) = 1: {1,3,4,5,6,7,8,9,10,11}.
a(12) = 5: {1,2,3,4,5,7,9,10,11,12}, {1,2,3,4,6,7,8,10,11,12}, {1,2,3,5,6,7,8,9,11,12}, {1,2,4,5,6,7,8,9,10,12}, {1,3,4,5,6,7,8,9,10,11}.

Links

Crossrefs

Column k=10 of A281871.

Programs

  • Maple
    b:= proc(n, i, t) option remember;
      `if`(i(t+1)*(2*i-t)/2, 0,
      `if`(i>n, 0, b(n-i, i-1, t-1))+b(n, i-1, t))))
    end:
a:= proc(n) option remember; `if`(n<0, 0, a(n-1)+add(
       b(j^2-n, n-1, 9), j=isqrt(n-45)..isqrt(10*n-45)))
    end:
seq(a(n), n=10..60);

A281965 Number of sets of exactly n positive integers <= n+2 having a square element sum.

Original entry on oeis.org

1, 1, 1, 2, 2, 2, 3, 4, 3, 3, 5, 4, 4, 5, 7, 5, 5, 9, 6, 6, 8, 9, 7, 7, 13, 8, 8, 12, 11, 9, 10, 15, 10, 10, 16, 13, 11, 14, 17, 12, 12, 20, 14, 13, 18, 19, 14, 15, 24, 15, 15, 22, 20, 16, 19, 26, 17, 17, 27, 20, 18, 23, 27, 19, 19, 33, 20, 20, 28, 27, 21, 23
Offset: 0

Views

Author

Alois P. Heinz, Feb 03 2017

Keywords

Examples

			a(7) = 4: {1,2,3,6,7,8,9}, {1,2,4,5,7,8,9}, {1,3,4,5,6,8,9}, {2,3,4,5,6,7,9}.
a(8) = 3: {1,2,3,4,5,6,7,8}, {1,3,5,6,7,8,9,10}, {2,3,4,6,7,8,9,10}.
a(9) = 3: {1,2,3,4,5,6,7,10,11}, {1,2,3,4,5,6,8,9,11}, {1,2,3,4,5,7,8,9,10}.

Links

Crossrefs

A diagonal of A281871.

Formula

a(n) = A281871(n+2,n).

A281966 Number of sets of exactly n positive integers <= n+3 having a square element sum.

Original entry on oeis.org

1, 2, 2, 3, 5, 6, 7, 10, 13, 14, 16, 21, 25, 24, 31, 37, 37, 40, 50, 55, 51, 64, 74, 69, 77, 92, 95, 89, 111, 122, 110, 127, 146, 145, 139, 171, 181, 161, 191, 213, 202, 203, 243, 250, 222, 270, 292, 264, 285, 328, 326, 296, 362, 381, 335, 383, 425, 407, 388
Offset: 0

Views

Author

Alois P. Heinz, Feb 03 2017

Keywords

Examples

			a(3) = 3: {1,2,6}, {1,3,5}, {2,3,4}.
a(4) = 5: {1,2,6,7}, {1,3,5,7}, {1,4,5,6}, {2,3,4,7}, {2,3,5,6}.
a(5) = 6: {1,2,3,4,6}, {1,3,6,7,8}, {1,4,5,7,8}, {2,3,5,7,8}, {2,4,5,6,8}, {3,4,5,6,7}.

Links

Crossrefs

A diagonal of A281871.

Formula

a(n) = A281871(n+3,n).

A281967 Number of sets of exactly n positive integers <= n+4 having a square element sum.

Original entry on oeis.org

1, 2, 3, 5, 8, 13, 19, 25, 34, 47, 58, 70, 92, 113, 130, 156, 194, 218, 246, 299, 343, 373, 430, 508, 543, 596, 701, 765, 813, 920, 1047, 1090, 1181, 1365, 1436, 1509, 1697, 1865, 1915, 2068, 2349, 2411, 2522, 2832, 3017, 3076, 3331, 3705, 3743, 3918, 4389
Offset: 0

Views

Author

Alois P. Heinz, Feb 03 2017

Keywords

Examples

			a(2) = 3: {1,3}, {3,6}, {4,5}.
a(3) = 5: {1,2,6}, {1,3,5}, {2,3,4}, {3,6,7}, {4,5,7}.
a(4) = 8: {1,2,5,8}, {1,2,6,7}, {1,3,4,8}, {1,3,5,7}, {1,4,5,6}, {2,3,4,7}, {2,3,5,6}, {4,6,7,8}.

Links

Crossrefs

A diagonal of A281871.

Formula

a(n) = A281871(n+4,n).

A281968 Number of sets of exactly n positive integers <= n+5 having a square element sum.

Original entry on oeis.org

1, 2, 4, 8, 14, 24, 39, 60, 86, 121, 171, 228, 294, 387, 499, 614, 762, 953, 1152, 1362, 1654, 1979, 2280, 2678, 3167, 3628, 4117, 4798, 5498, 6109, 6968, 7967, 8824, 9793, 11127, 12382, 13462, 15088, 16845, 18230, 19981, 22294, 24272, 26047, 28849, 31616
Offset: 0

Views

Author

Alois P. Heinz, Feb 03 2017

Keywords

Examples

			a(2) = 4: {1,3}, {2,7}, {3,6}, {4,5}.
a(3) = 8: {1,2,6}, {1,3,5}, {1,7,8}, {2,3,4}, {2,6,8}, {3,5,8}, {3,6,7}, {4,5,7}.
a(4) = 14: {1,2,4,9}, {1,2,5,8}, {1,2,6,7}, {1,3,4,8}, {1,3,5,7}, {1,4,5,6}, {1,7,8,9}, {2,3,4,7}, {2,3,5,6}, {2,6,8,9}, {3,5,8,9}, {3,6,7,9}, {4,5,7,9}, {4,6,7,8}.

Links

Crossrefs

A diagonal of A281871.

Formula

a(n) = A281871(n+5,n).

A281969 Number of sets of exactly n positive integers <= n+6 having a square element sum.

Original entry on oeis.org

1, 2, 5, 11, 23, 43, 74, 124, 197, 296, 434, 627, 875, 1188, 1600, 2128, 2755, 3522, 4511, 5661, 6983, 8637, 10610, 12781, 15343, 18497, 21937, 25751, 30416, 35702, 41266, 47772, 55531, 63578, 72405, 83101, 94662, 106544, 120507, 136663, 152742, 170490, 191873
Offset: 0

Views

Author

Alois P. Heinz, Feb 03 2017

Keywords

Examples

			a(4) = 23: {1,2,3,10}, {1,2,4,9}, {1,2,5,8}, {1,2,6,7}, {1,3,4,8}, {1,3,5,7}, {1,4,5,6}, {1,5,9,10}, {1,6,8,10}, {1,7,8,9}, {2,3,4,7}, {2,3,5,6}, {2,4,9,10}, {2,5,8,10}, {2,6,7,10}, {2,6,8,9}, {3,4,8,10}, {3,5,7,10}, {3,5,8,9}, {3,6,7,9}, {4,5,6,10}, {4,5,7,9}, {4,6,7,8}.

Links

Crossrefs

A diagonal of A281871.

Programs

Formula

a(n) = A281871(n+6,n).

A281970 Number of sets of exactly n positive integers <= n+7 having a square element sum.

Original entry on oeis.org

1, 2, 6, 15, 34, 71, 134, 238, 405, 660, 1030, 1559, 2310, 3336, 4691, 6500, 8886, 11899, 15709, 20584, 26624, 33926, 42974, 54080, 67172, 82800, 101787, 124031, 149660, 180251, 216171, 256730, 303737, 359036, 421356, 491196, 572792, 665539, 767239, 883380
Offset: 0

Views

Author

Alois P. Heinz, Feb 03 2017

Keywords

Examples

			a(3) = 15: {1,2,6}, {1,3,5}, {1,5,10}, {1,6,9}, {1,7,8}, {2,3,4}, {2,4,10}, {2,5,9}, {2,6,8}, {3,4,9}, {3,5,8}, {3,6,7}, {4,5,7}, {6,9,10}, {7,8,10}.

Links

Crossrefs

A diagonal of A281871.

Formula

a(n) = A281871(n+7,n).

A281971 Number of sets of exactly n positive integers <= n+8 having a square element sum.

Original entry on oeis.org

1, 3, 7, 20, 49, 110, 227, 435, 786, 1358, 2259, 3621, 5627, 8538, 12655, 18318, 26049, 36487, 50236, 68131, 91412, 121207, 158659, 205768, 264786, 337240, 425738, 534408, 665866, 822789, 1011364, 1237211, 1502645, 1814854, 2184786, 2615980, 3114026, 3695678
Offset: 0

Views

Author

Alois P. Heinz, Feb 03 2017

Keywords

Examples

			a(2) = 7: {1,3}, {1,8}, {2,7}, {3,6}, {4,5}, {6,10}, {7,9}.
a(3) = 20: {1,2,6}, {1,3,5}, {1,4,11}, {1,5,10}, {1,6,9}, {1,7,8}, {2,3,4}, {2,3,11}, {2,4,10}, {2,5,9}, {2,6,8}, {3,4,9}, {3,5,8}, {3,6,7}, {4,5,7}, {4,10,11}, {5,9,11}, {6,8,11}, {6,9,10}, {7,8,10}.

Links

Crossrefs

A diagonal of A281871.

Formula

a(n) = A281871(n+8,n).
Previous Showing 11-20 of 24 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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