A253920 Indices of centered octagonal numbers (A016754) which are also heptagonal numbers (A000566).

1, 5, 39, 760, 6494, 55518, 1095199, 9363623, 80056197, 1579275478, 13502337152, 115440979836, 2277314143357, 19470360808841, 166465812866595, 3283885415444596, 28076246784010850, 240043586712649434, 4735360491756963355, 40485928392182836139

Offset

1,2

Comments

Also positive integers y in the solutions to 5*x^2 - 8*y^2 - 3*x + 8*y - 2 = 0, the corresponding values of x being A046195.

Links

Colin Barker, Table of n, a(n) for n = 1..950

Index entries for linear recurrences with constant coefficients, signature (1,0,1442,-1442,0,-1,1).

Formula

a(n) = a(n-1)+1442*a(n-3)-1442*a(n-4)-a(n-6)+a(n-7).

G.f.: x*(4*x^5+34*x^4+721*x^3-34*x^2-4*x-1) / ((x-1)*(x^6-1442*x^3+1)).

Example

5 is in the sequence because the 5th centered octagonal number is 81, which is also the 6th heptagonal number.

Mathematica

CoefficientList[Series[(4 x^5 + 34 x^4 + 721 x^3 - 34 x^2 -4 x - 1)/((x-1) (x^6 - 1442 x^3 + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 20 2015 *)
LinearRecurrence[{1, 0, 1442, -1442, 0, -1, 1}, {1, 5, 39, 760, 6494, 55518, 1095199}, 20] (* Harvey P. Dale, Jul 04 2017 *)

Prog

(PARI) Vec(x*(4*x^5+34*x^4+721*x^3-34*x^2-4*x-1)/((x-1)*(x^6-1442*x^3+1)) + O(x^100))
(Magma) I:=[1, 5, 39, 760, 6494, 55518, 1095199]; [n le 7 select I[n] else Self(n-1)+1442*Self(n-3)-1442*Self(n-4)-Self(n-6)+Self(n-7): n in [1..25]]; // Vincenzo Librandi, Jan 20 2015

Crossrefs

Cf. A000566, A016754, A046195, A036354.

Sequence in context: A193118 A227636 A118991 * A156378 A220061 A299815

Adjacent sequences: A253917 A253918 A253919 * A253921 A253922 A253923

Keyword

nonn,easy

Author

Colin Barker, Jan 19 2015

Extensions

Corrected by Vincenzo Librandi, Jan 20 2015

Status

approved