A061208 Numbers which can be expressed as sum of distinct triangular numbers (A000217).

1, 3, 4, 6, 7, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77

Offset: 1

Author

Amarnath Murthy, Apr 21 2001

Keywords

• nonn

Comments

These numbers were called "almost-triangular" numbers during the Peru's Selection Test for the XII IberoAmerican Olympiad (1998). All numbers >= 34 are almost-triangular: see link. [Bernard Schott, Feb 04 2013]

Examples

			25 = 1 + 3 + 6 + 15
		

Links

• R. E. Woodrow, The Olympiad Corner, No. 198, Crux Mathematicorum, v25-n4(2002), 207-208, exercise 2.

Crossrefs

Cf. A000217, A007294, A051611, A051533. Complement of A053614.

Programs

Maple

gf := product(1+x^(j*(j+1)/2), j=1..100): s := series(gf, x, 200): for i from 1 to 200 do if coeff(s, x, i) > 0 then printf(`%d,`,i) fi:od:

Extensions

Corrected and extended by James Sellers, Apr 24 2001