A372070 Triangular numbers that are 2 mod 4.

6, 10, 66, 78, 190, 210, 378, 406, 630, 666, 946, 990, 1326, 1378, 1770, 1830, 2278, 2346, 2850, 2926, 3486, 3570, 4186, 4278, 4950, 5050, 5778, 5886, 6670, 6786, 7626, 7750, 8646, 8778, 9730, 9870, 10878, 11026, 12090, 12246, 13366, 13530, 14706, 14878, 16110, 16290, 17578, 17766, 19110

Offset

1,1

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Formula

From Elmo R. Oliveira, Apr 10 2026: (Start)

a(n) = 2*A372718(n) = A000217(A047457(n)).

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n > 5.

a(n) = [x^n] 2*x*(3 + 2*x + 22*x^2 + 2*x^3 + 3*x^4)/((1-x)^3*(1+x)^2). (End)

Mathematica

LinearRecurrence[{1, 2, -2, -1, 1}, {6, 10, 66, 78, 190}, 50] (* Paolo Xausa, Apr 16 2026 *)

Crossrefs

Cf. A000217, A047457, A372718.

Sequence in context: A136847 A250106 A230827 * A111484 A119041 A105157

Adjacent sequences: A372067 A372068 A372069 * A372071 A372072 A372073

Keyword

nonn,easy

Author

N. J. A. Sloane, May 25 2024

Status

approved