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

1,2

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]

Links

Table of n, a(n) for n=1..71.

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

Example

25 = 1 + 3 + 6 + 15

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:

Crossrefs

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

Sequence in context: A233334 A320300 A070762 * A325439 A183860 A298109

Adjacent sequences: A061205 A061206 A061207 * A061209 A061210 A061211

Keyword

nonn

Author

Amarnath Murthy, Apr 21 2001

Extensions

Corrected and extended by James A. Sellers, Apr 24 2001

Status

approved