A254284 Indices of centered triangular numbers (A005448) which are also hexagonal numbers (A000384).

1, 36, 133, 6888, 25705, 1336140, 4986541, 259204176, 967363153, 50284273908, 187663465045, 9754889933880, 36405744855481, 1892398362898716, 7062526838498173, 367115527512416928, 1370093800923789985, 71218519939045985220, 265791134852376758821

Offset: 1

Author

Colin Barker, Jan 28 2015

Keywords

• nonn
• easy

Comments

Also positive integers y in the solutions to 4*x^2 - 3*y^2 - 2*x + 3*y - 2 = 0, the corresponding values of x being A254283.

Examples

			36 is in the sequence because the 36th centered triangular number is 1891, which is also the 31st hexagonal number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..875
• Index entries for linear recurrences with constant coefficients, signature (1,194,-194,-1,1).

Crossrefs

Cf. A000384, A005448, A254283, A254285.

Programs

Mathematica

LinearRecurrence[{1,194,-194,-1,1},{1,36,133,6888,25705},20] (* Harvey P. Dale, Nov 11 2020 *)

PARI

Vec(x*(35*x^3+97*x^2-35*x-1)/((x-1)*(x^2-14*x+1)*(x^2+14*x+1)) + O(x^100))

Formula

a(n) = a(n-1)+194*a(n-2)-194*a(n-3)-a(n-4)+a(n-5).

G.f.: x*(35*x^3+97*x^2-35*x-1) / ((x-1)*(x^2-14*x+1)*(x^2+14*x+1)).