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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.

LINKS

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

P. De Geest, Palindromic Tetrahedrals

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[ # ]&] [From 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

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Last modified November 28 02:24 EST 2014. Contains 250286 sequences.