Term

Centered Triangular

Centered figurate numbers — a dot ringed by triangles: (3k²−3k+2)/2 → 1, 4, 10, 19, 31, 46, ….

80 numbers tagged.

A centered triangular number has a dot at the centre surrounded by triangular rings: 1, 4, 10, 19, 31, 46, 64, 85, 109. The formula is \((3k^2 - 3k + 2)/2\).

They complete, with the [[centered-square]] and [[centered-hexagonal]] numbers, the family of centered polygonal numbers — distinct from the ordinary [[triangular]] numbers, which build from a corner rather than a centre. Every centered triangular number leaves remainder 1 when divided by 3.

4 10 19 31 46 64 85 109 136 166 199 235 274 316 361 409 460 514 571 631 694 760 829 901 976 1,054 1,135 1,219 1,306 1,396 1,489 1,585 1,684 1,786 1,891 1,999 2,341 2,971 3,529 4,621 4,789 7,039 7,669 8,779 9,721 10,459 10,711 13,681 14,851 16,069 16,381 17,659 20,011 20,359 23,251 25,939 27,541 29,191 29,611 31,321 34,429 36,739 40,099 40,591 42,589 44,119 48,871 51,061 53,299 55,009 57,331 62,119 62,731 69,661 70,309 72,271 72,931 74,929 89,671 98,689

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