A052346 Smallest number which is the sum of two positive triangular numbers in exactly n different ways.

1, 2, 16, 81, 471, 1056, 1381, 11781, 6906, 17956, 34531, 123256, 40056, 4462656, 305256, 448906, 200281, 1957231, 520731, 10563906, 1001406, 11222656, 539550781, 3454506, 1482081, 75865156, 7172606106, 8852431, 25035156, 334020781, 13018281, 38531031, 7410406, 7014160156

Offset

0,2

Comments

From Chai Wah Wu, Oct 20 2023: (Start)

Other terms:

a(35) = 42980356

a(36) = 19267056

a(38) = 1289707656

a(39) = 2782318906

a(40) = 37052031

a(41) = 256720506

a(42) = 325457031

a(45) = 221310781

a(47) = 550240551

a(48) = 60765331

a(50) = 2200089531

a(54) = 327539956

a(56) = 926300781

a(59) = 7629645156

a(60) = 481676406

a(63) = 4598740656

a(64) = 303826656

a(68) = 6418012656

a(71) = 4579579956

a(72) = 789949306

a(80) = 1519133281

a(81) = 9498658731

a(84) = 12041910156

a(90) = 8188498906

a(96) = 3220562556

a(108) = 13429138206

(End)

Links

Table of n, a(n) for n=0..33.

Example

a(4) = 471 because 471 is the sum of two positive triangular numbers in exactly 4 different ways (as 300+171, 351+120, 435+36, and 465 + 6), and there is no smaller number that has this property.

Crossrefs

Cf. A000217, A052343, A052344, A052345, A052347, A052348, A053587, A064816.

Sequence in context: A012684 A234004 A053587 * A207482 A207880 A207263

Adjacent sequences: A052343 A052344 A052345 * A052347 A052348 A052349

Keyword

nonn

Author

Christian G. Bower, Jan 23 2000

Extensions

a(27), a(28) = 8852431, 25035156; a(26) not yet found

a(26) from Donovan Johnson, Nov 17 2008

Name edited (added the qualifier "positive"), example edited, and a(29)-a(32) added by Jon E. Schoenfield, Jul 16 2017

a(33) from Chai Wah Wu, Oct 20 2023

Status

approved