A274682 Numbers n such that 8*n-1 is a triangular number.

2, 7, 29, 44, 88, 113, 179, 214, 302, 347, 457, 512, 644, 709, 863, 938, 1114, 1199, 1397, 1492, 1712, 1817, 2059, 2174, 2438, 2563, 2849, 2984, 3292, 3437, 3767, 3922, 4274, 4439, 4813, 4988, 5384, 5569, 5987, 6182, 6622, 6827, 7289, 7504, 7988, 8213, 8719

Offset

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = (5+3*(-1)^n-2*(8+3*(-1)^n)*n+16*n^2)/4.

a(n) = (8*n^2-11*n+4)/2 for n even.

a(n) = (8*n^2-5*n+1)/2 for n odd.

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

G.f.: x*(2+5*x+18*x^2+5*x^3+2*x^4) / ((1-x)^3*(1+x)^2).

Example

2 is in the sequence since 8*2 - 1 = 15, and 15 = 1 + 2 + 3 + 4 + 5 is a triangular number. - Michael B. Porter, Jul 03 2016

Mathematica

Table[(5 + 3 (-1)^n - 2 (8 + 3 (-1)^n) n + 16 n^2)/4, {n, 47}] (* or *)
Rest@ CoefficientList[Series[x (2 + 5 x + 18 x^2 + 5 x^3 + 2 x^4)/((1 - x)^3 (1 + x)^2), {x, 0, 47}], x] (* Michael De Vlieger, Jul 02 2016 *)

Prog

(PARI) isok(n) = ispolygonal(8*n-1, 3)
(PARI) select(n->ispolygonal(8*n-1, 3), vector(10000, n, n-1))
(PARI) Vec(x*(2+5*x+18*x^2+5*x^3+2*x^4)/((1-x)^3*(1+x)^2) + O(x^100))

Crossrefs

Cf. A000124 (n-1), A174114 (2*n-1), A213399 (4*n-1), A069099 (7*n-1).

Sequence in context: A180448 A116968 A162172 * A359633 A339868 A181758

Adjacent sequences: A274679 A274680 A274681 * A274683 A274684 A274685

Keyword

nonn,easy

Author

Colin Barker, Jul 02 2016

Status

approved