A185253 a(n) = A185128(n) - A185129(n).

6, 66, 325, 210, 1596, 2701, 1326, 903, 1225, 16836, 6903, 82621, 141778, 181503, 63546, 52975, 354903, 10440, 13530, 405450, 7140, 989121, 1329265, 511566, 668746, 437580, 2102275, 2001000, 2469753, 3229611, 1428895, 3096316, 1963171, 6843150, 856086, 4276350

Offset: 1

Author

Martin Renner, Jan 20 2012

Keywords

• nonn

References

• Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966, p. 197, no. 8.

Links

• N. J. A. Sloane, Annotated scan of Beiler's Table 81, based on page 197 of Beiler's "Recreations in the Theory of Numbers: The Queen of Mathematics Entertains", New York, Dover, First ed., 1964.

Crossrefs

Cf. A000217, A185128, A185129, A185223, A185233, A185243, A185257, A185258.

Programs

Mathematica

kmax=2000; TriangularQ[n_]:=IntegerQ[(Sqrt[1+8n]-1)/2]; A000217[n_]:=n(n+1)/2; a={}; For[k=1, k<=kmax, k++, For[h=1, A000217[h]<A000217[k], h++, If[TriangularQ[d=A000217[k] - A000217[h]] && TriangularQ[A000217[k]+A000217[h]], AppendTo[a,d]]]]; a (* Stefano Spezia, Sep 02 2024 *)

PARI

lista(nn) = {v = vector(nn, n, n*(n+1)/2); for (n=2, nn, for (k=1, n-1, if (ispolygonal(v[n]+v[k], 3) && ispolygonal(v[n]-v[k], 3), print1(v[n]-v[k], ", "));););} \\ Michel Marcus, Jan 08 2015

Extensions

Edited by N. J. A. Sloane, Dec 28 2024 (replaced definition with simpler and more explicit formula from Michel Marcus, Jan 08 2015)