A267297 Square triangular numbers that are the sum of 2 nonzero nonconsecutive triangular numbers.

1225, 41616, 1413721, 1631432881, 55420693056, 1882672131025, 63955431761796, 2172602007770041, 73804512832419600, 2507180834294496361, 85170343853180456676, 2893284510173841030625, 98286503002057414584576, 3338847817559778254844961, 113422539294030403250144100

Offset

1,1

Comments

Subsequence of A001110. Conjecture: except for the terms 0, 1, 36, 48024900, the sequence is identical to A001110.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..50

Formula

Conjectures from Colin Barker, Mar 03 2016: (Start)

a(n) = 35*a(n-1)-35*a(n-2)+a(n-3) for n>6.

G.f.: x*(1225-1259*x+36*x^2+1583407981*x^3-1630019160*x^4+46611179*x^5) / ((1-x)*(1-34*x+x^2)).

(End)

Example

98286503002057414584576 = 313506783024^2 = 443365544448*443365544449/2 = 313468166681*313468166682/2 + 313545394610*313545394611/2.

Crossrefs

Cf. A001110, A229134.

Sequence in context: A183665 A250848 A014795 * A151657 A218273 A046177

Adjacent sequences: A267294 A267295 A267296 * A267298 A267299 A267300

Keyword

nonn

Author

Chai Wah Wu, Feb 26 2016

Status

approved