A081975 Triangular number pertaining to A081974. a(n) = A081974(n)*A081974(n+1).

3, 6, 10, 45, 36, 28, 91, 78, 66, 231, 210, 120, 276, 1035, 630, 378, 1431, 1378, 780, 990, 528, 496, 465, 300, 820, 3321, 3240, 2080, 5356, 5253, 1275, 1225, 1176, 1128, 4371, 4278, 4186, 5460, 4560, 11476, 11325, 2775, 666, 2016, 12880, 6555, 1596

Offset

1,1

Comments

A subset of A000217. - R. J. Mathar, Apr 05 2007

Links

Table of n, a(n) for n=1..47.

Maple

isA000217 := proc(n) local t; t := (sqrt(1+8*n)-1)/2 ; type(t, 'integer'); end: A081974 := proc(nmax) local a, n, prodset; a := [1, 3] ; prodset := {3} ; while nops(a) < nmax do n := 2 ; while n in a or n*op(-1, a) in prodset or isA000217(n*op(-1, a)) = false do n := n+1 ; od ; prodset := prodset union { n*op(-1, a) } ; a := [op(a), n] ; od ; RETURN(a) ; end: A081975 := proc(nmax) local a ; a081974 := A081974(nmax) ; a := [] ; for i from 2 to nops(a081974) do a := [op(a), op(i, a081974)*op(i-1, a081974)] ; od ; RETURN(a) ; end: a := A081975(100) ; # R. J. Mathar, Apr 05 2007

Mathematica

istriang[n_] := With[{x = Floor[Sqrt[2*n]]}, n == x*(x + 1)/2];
nmax = 47;
Clear[b, used, tris];
b[_] = 0; used[_] = 0; tris[_] = 0; b[1] = 1; used[1] = 1;
For[i = 2, i <= nmax+1, i++, f = b[i-1]; j = 2; While[used[j] == 1 || !istriang[f*j] || tris[f*j] == 1, j++]; b[i] = j; used[j] = 1; tris[f*j] = 1];
a[n_] := b[n]*b[n + 1];
Table[a[n], {n, 1, nmax}] (* Jean-François Alcover, May 23 2024, after PARI code in A081974 *)

Crossrefs

Cf. A081974, A081976, A081977.

Sequence in context: A339783 A317361 A048089 * A160965 A069708 A061455

Adjacent sequences: A081972 A081973 A081974 * A081976 A081977 A081978

Keyword

nonn

Author

Amarnath Murthy, Apr 03 2003

Extensions

More terms from R. J. Mathar, Apr 05 2007

Status

approved