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A274682 Numbers n such that 8*n-1 is a triangular number. 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A181758 A285790 A083016

Adjacent sequences:  A274679 A274680 A274681 * A274683 A274684 A274685

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Jul 02 2016

STATUS

approved

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Last modified September 15 20:42 EDT 2019. Contains 327087 sequences. (Running on oeis4.)