A254283 Indices of hexagonal numbers (A000384) which are also centered triangular numbers (A005448).

1, 31, 115, 5965, 22261, 1157131, 4318471, 224477401, 837761065, 43547458615, 162521328091, 8447982493861, 31528299888541, 1638865056350371, 6116327657048815, 317931372949478065, 1186536037167581521, 61677047487142394191, 230181874882853766211

Offset

1,2

Comments

Also positive integers x in the solutions to 4*x^2 - 3*y^2 - 2*x + 3*y - 2 = 0, the corresponding values of y being A254284.

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).

Formula

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

G.f.: -x*(x^4+30*x^3-110*x^2+30*x+1) / ((x-1)*(x^2-14*x+1)*(x^2+14*x+1)).

Example

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

Prog

(PARI) Vec(-x*(x^4+30*x^3-110*x^2+30*x+1)/((x-1)*(x^2-14*x+1)*(x^2+14*x+1)) + O(x^100))

Crossrefs

Cf. A000384, A005448, A254284, A254285.

Sequence in context: A142228 A304241 A204735 * A010019 A256650 A131550

Adjacent sequences: A254280 A254281 A254282 * A254284 A254285 A254286

Keyword

nonn,easy

Author

Colin Barker, Jan 28 2015

Status

approved