login
This site is supported by donations to The OEIS Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A281871 Number T(n,k) of k-element subsets of [n] having a square element sum; triangle T(n,k), n>=0, 0<=k<=n, read by rows. 24
1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 2, 1, 1, 0, 1, 2, 2, 2, 0, 0, 1, 2, 3, 3, 2, 1, 0, 1, 2, 4, 5, 5, 2, 1, 0, 1, 2, 5, 8, 8, 6, 3, 0, 1, 1, 3, 6, 11, 14, 13, 7, 4, 1, 0, 1, 3, 7, 15, 23, 24, 19, 10, 3, 1, 0, 1, 3, 8, 20, 34, 43, 39, 25, 13, 3, 1, 0, 1, 3, 9, 26, 49, 71, 74, 60, 34, 14, 5, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,12

LINKS

Alois P. Heinz, Rows n = 0..200, flattened

FORMULA

T(n,n) = 1 for n in { A001108 }, T(n,n) = 0 otherwise.

T(n,n-1) = 1 for n in { A214857 }, T(n,n-1) = 0 for n in { A214858 }.

EXAMPLE

T(7,0) = 1: {}.

T(7,1) = 2: {1}, {4}.

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

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

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

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

T(7,6) = 1: {1,2,4,5,6,7}.

T(7,7) = 0.

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

Triangle T(n,k) begins:

  1;

  1, 1;

  1, 1, 0;

  1, 1, 1,  0;

  1, 2, 1,  1,  0;

  1, 2, 2,  2,  0,  0;

  1, 2, 3,  3,  2,  1,  0;

  1, 2, 4,  5,  5,  2,  1,  0;

  1, 2, 5,  8,  8,  6,  3,  0,  1;

  1, 3, 6, 11, 14, 13,  7,  4,  1,  0;

  1, 3, 7, 15, 23, 24, 19, 10,  3,  1, 0;

  1, 3, 8, 20, 34, 43, 39, 25, 13,  3, 1, 0;

  1, 3, 9, 26, 49, 71, 74, 60, 34, 14, 5, 0, 0;

MAPLE

b:= proc(n, s) option remember; expand(`if`(n=0,

      `if`(issqr(s), 1, 0), b(n-1, s)+x*b(n-1, s+n)))

    end:

T:= n-> (p-> seq(coeff(p, x, i), i=0..n))(b(n, 0)):

seq(T(n), n=0..16);

MATHEMATICA

b[n_, s_] := b[n, s] = Expand[If[n == 0, If[IntegerQ @ Sqrt[s], 1, 0], b[n - 1, s] + x*b[n - 1, s + n]]];

T[n_] := Function[p, Table[Coefficient[p, x, i], {i, 0, n}]][b[n, 0]];

Table[T[n], {n, 0, 10}] // Flatten (* Jean-Fran├žois Alcover, Jun 03 2018, from Maple *)

CROSSREFS

Columns k=0-10 give: A000012, A000196, A176615, A281706, A281864, A281865, A281866, A281867, A281868, A281869, A281870.

Main diagonal is characteristic function of A001108.

Diagonals T(n+k,n) for k=2-10 give: A281965, A281966, A281967, A281968, A281969, A281970, A281971, A281972, A281973.

Row sums give A126024.

T(2n,n) gives A281872.

Cf. A000217, A000290, A007318, A214857, A214858, A278339, A281994, A284249.

Sequence in context: A259538 A099314 A214341 * A131334 A004602 A247418

Adjacent sequences:  A281868 A281869 A281870 * A281872 A281873 A281874

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Jan 31 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 19 19:49 EST 2019. Contains 319309 sequences. (Running on oeis4.)