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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A027568 Numbers that are both triangular and tetrahedral. 6
0, 1, 10, 120, 1540, 7140 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

Avanesov, E. T.; Solution of a problem on figurate numbers. (Russian) Acta Arith. 12 1966/1967 409-420.

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 10, p. 3 ; Entry 119, p. 41, Ellipses, Paris 2008.

L. J. Mordell, Diophantine Equations, Ac. Press, p. 258.

J. Roberts, The Lure of the Integers, page 53.

LINKS

Table of n, a(n) for n=1..6.

P. De Geest, Palindromic Tetrahedrals

M. Gardner, Letter to N. J. A. Sloane, circa Aug 11 1980, concerning A1110, A27568, A39596, etc.

Eric Weisstein's World of Mathematics, Tetrahedral Number

MAPLE

{seq(binomial(i, 3), i=0..100000) } intersect {seq(binomial(k, 2), k= 0..100000)}; # Zerinvary Lajos, Apr 26 2008

MATHEMATICA

f3[n_]:=n*(n+1)*(n+2)/6; TriangularNumberQ[n_]:=Floor[Sqrt[2*n]]*(Floor[Sqrt[2*n]]+1)/2==n; Select[f3[Range[5! ]], TriangularNumberQ[ # ]&] (* Vladimir Joseph Stephan Orlovsky, Feb 16 2010 *)

With[{trno=Accumulate[Range[0, 1000]]}, Intersection[trno, Accumulate[ trno]]] (* Harvey P. Dale, May 25 2014 *)

PROG

(PARI) for(n=0, 1e3, if(ispolygonal(t=n*(n+1)*(n+2)/6, 3), print1(t", "))) \\ Charles R Greathouse IV, Apr 07 2013

CROSSREFS

Intersection of A000217 and A000292.

Cf. A102349, A102461, A102772.

Sequence in context: A182605 A024127 A005949 * A034255 A051582 A122420

Adjacent sequences:  A027565 A027566 A027567 * A027569 A027570 A027571

KEYWORD

nonn,fini,full

AUTHOR

Patrick De Geest

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified July 28 09:29 EDT 2015. Contains 260066 sequences.